Publications – Andrei Martinez‑Finkelshtein

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ORCID Profile: 0000-0001-9421-5624
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Scopus Author ID: 6701672042
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Preprints

Recent preprints are available on my arXiv page.

Journal Articles

Zeros of generalized hypergeometric polynomials via finite free convolution: Applications to multiple orthogonality,
A. Martinez-Finkelshtein, R. Morales, D. Perales, Constr. Approximation, doi 10.1007/s00365-025-09703-w. Also preprint arXiv:2404.11479.
Real roots of hypergeometric polynomials via finite free convolution
A. Martinez-Finkelshtein, R. Morales, D. Perales, International Mathematics Research Notices, Volume 2024, Issue 16, August 2024, Pages 11642–11687, https://doi.org/10.1093/imrn/rnae120. Also preprint arXiv:2309.10970.
Interlacing and monotonicity of zeros of Angelesco-Jacobi polynomials
A. Martinez-Finkelshtein, R. Morales, Pure and Applied Functional Analysis 9 (5), 1259-1279, 2024. Also preprint arXiv:2310.06688.
Electrostatic partners and zeros of orthogonal and multiple orthogonal polynomials
A. Martínez-Finkelshtein, R. Orive, J. Sánchez-Lara, Constructive Approximation 58 (2023), 271–342, DOI 10.1007/s00365-022-09609-x. Also preprint arXiv math.2203.01419.
Poncelet-Darboux, Kippenhahn, and Szegő: interactions between projective geometry, matrices and orthogonal polynomials
M. Hunziker, A. Martinez-Finkelshtein, T. Poe, B. Simanek, Journal of Mathematical Analysis and Applications 511 (1), 126049. Also preprint arXiv math.2101.12165.
Spectral curves, variational problems, and the hermitian matrix model with external source
A. Martinez-Finkelshtein, G. Silva, Comm. Math. Physics 383 (3), (2021) 2163-2242, https://doi.org/10.1007/s00220-021-03999-y. Also preprint ArXiv math:1907.08108.
On foci of ellipses inscribed in cyclic polygons
M. Hunziker, A. Martinez-Finkelshtein, T. Poe, B. Simanek, in F. Gesztesy, A. Martinez-Finkelshtein (eds.), "From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory", Operator Theory: Advances and Applications 285, https://doi.org/10.1007/978-3-030-75425-9_12, pages 213-238. Also preprint arXiv math.2101.12638.
Complementary Romanovski–Routh Polynomials, Orthogonal Polynomials on the Unit Circle, and Extended Coulomb Wave Functions
Martínez-Finkelshtein, A., Silva Ribeiro, L.L., Sri Ranga, A. et al., Results Math (2020) 75: 42. https://doi.org/10.1007/s00025-020-1167-8.
Robust keratoconus detection with Bayesian network classifier for Placido-based corneal indices
G. M. Castro-Luna, A. Martínez-Finkelshtein, D. Ramos-López, Contact Lens & Anterior Eye 43 (2020), 366-372.

Complementary Romanovski-Routh polynomials: From orthogonal polynomials on the unit circle to Coulomb wave functions
A. Martínez-Finkelshtein, L.L. Silva Ribeiro, A. S. Ranga, M. Tyaglov, Proceedings of the AMS 147 (6) (2019), 2625–2640, https://doi.org/10.1090/proc/14423. Also preprint arXiv math.1806.02232.
Critical measures for vector energy: asymptotics of non-diagonal multiple orthogonal polynomials for a cubic weight
A. Martinez-Finkelshtein, G. Silva, Advances in Mathematics 349 (2019), 246-315. Also preprint ArXiv math:1805.01748.
Poncelet's Theorem, Paraorthogonal Polynomials and the Numerical Range of Compressed Multiplication Operators
A. Martínez-Finkelshtein, Brian Simanek, Barry Simon, Advances in Mathematics 349 (2019), 992-1035. Also preprint arXiv math.1810.13357.
Extreme zeros in a sequence of para-orthogonal polynomials and bounds for the support of the measure
A. Martínez-Finkelshtein, A. S. Ranga, D. O. Veronese, Mathematics of Computation 87 (309) (2018), 261-288. Also preprint arXiv math.1505.07788.
Christoffel formula for kernel polynomials on the unit circle
C. F. Bracciali, A. Martínez-Finkelshtein, A. S. Ranga, D. O. Veronese, J. Approximation Theory 235 (2018) 46–73. Also preprint arXiv math.1701.04995.
Some extremal problems of roots of orthogonal polynomials
C. Beltrán, F. Marcellán, A. Martínez-Finkelshtein, La Gaceta de la RSME 21 (2), 2018, 345-366. (in Spanish)
A semi-analytic approach to calculating the Strehl ratio for a circularly symmetric system. Part 1: static wavefronts
A. B. Castaño-Fernández, A. Martínez-Finkelshtein, and D. Robert Iskander, Optica Applicata XLVII (2) (2018), 201-210, doi 10.5277/oa180204.
A semi-analytic approach to calculating the Strehl ratio for a circularly symmetric system. Part 2: dynamic wavefronts
A. B. Castaño-Fernández, A. Martínez-Finkelshtein, and D. Robert Iskander, Optica Applicata XLVII (2) (2018), 211-223, doi 10.5277/oa180205.
Computation of 2D Fourier transforms and diffraction integrals using Gaussian radial basis functions
A. Martínez-Finkelshtein, D. Ramos-López, and D. Robert Iskander, Applied and Computational Harmonic Analysis 43 (3) (2017), 424-448, doi 10.1016/j.acha.2016.01.007. Also preprint arXiv math.1506.01670.
On Nikishin systems with discrete components and weak asymptotics of multiple orthogonal polynomials
A. Aptekarev, G. López-Lagomasino, A. Martínez-Finkelshtein, Uspekhi Mat. Nauk 72: 3(435) (2017), 3–64. English transl. in Russian Math. Surveys 72:3 (2017), 389–449. Also preprint arXiv math.1403.3729.
New Objective Refraction Metric based on Sphere Fitting to the Wavefront
M. Jaskulski, A. Martinez-Finkelshtein, and N. López-Gil, Journal of Ophthalmology, Volume 2017, Article ID 1909348, 9 pages.
Optimal sampling patterns for Zernike polynomials
D. Ramos-López, M. A. Sánchez-Granero, M. Fernández-Martínez, and A. Martínez-Finkelshtein, Applied Mathematics and Computation 274 (2016) 247-257. Also preprint arXiv math.1511.00449.
Trajectories of quadratic differentials for Jacobi polynomials with complex parameters
A. Martínez-Finkelshtein, P. Martínez-González, F. Thabet, Comput. Methods and Function Theory 16 (3) (2016), 347-364, doi 10.1007/s40315-015-0146-7. Also preprint arXiv math.1506.03434.
Asymptotics of type I Hermite–Padé polynomials for semiclassical functions
A. Martínez-Finkelshtein, E. A. Rakhmanov, S. P. Suetin, Contemp. Math. 661 (2016), 199-228. Also preprint arXiv math.1502.01202.
Average of elastic properties of the cornea
D. Guinovart-Sanjuán, R. Rodríguez-Ramos, R. Guinovart-Díaz, J. Bravo, A. Martínez-Finkelshtein, A. Conci, F. Lebon and S. Dumont, Conference Proceeding, 23rd ABCM International Congress of Mechanical Engineering, COBEM, December 6--11, 2015, Río de Janeiro, Brasil. DOI: 10.20906/CPS/COB-2015-0156.
What is... a multiple orthogonal polynomial?
A. Martínez-Finkelshtein and W. Van Assche, Notices of the AMS, October 2016, 647-649. Also preprint arXiv math.1707.09511.
From Mathematical Physics to Analysis: A Walk in Barry Simon's Mathematical Garden, II
F. Gesztesy, J. Avron, S. Jitomirskaya, D. Damanik, J. Breuer, Y. Last, and A. Martínez-Finkelshtein, Notices of the AMS 63 (8), September 2016, 878-889. DOI: http://dx.doi.org/10.1090/noti1412.
Heisenberg-like uncertainty measures for D-dimensional hydrogenic systems at large D
I.V. Toranzo, A. Martínez-Finkelshtein, J.S. Dehesa, J. Math. Phys. 57, 082109 (2016), doi 10.1063/1.4961322. Also preprint arXiv math.1609.01113.
Do orthogonal polynomials dream of symmetric curves?
A. Martinez-Finkelshtein, E. A. Rakhmanov, Foundations of Computational Mathematics (2016) 16:1697–1736, doi: 10.1007/s10208-016-9313-0. Also preprint arXiv math.1511.09175.
Critical measures for vector energy: global structure of trajectories of quadratic differentials
A. Martínez-Finkelshtein, G. Silva, Advances in Mathematics 302 (2016), 1137-1232. Also preprint Аrxiv math.1509.06704.
Phase transitions and equilibrium measures in random matrix models
A. Martínez-Finkelshtein, E. A. Rakhmanov, R. Orive, Comm. Math. Physics 333 (3) (2015), 1109-1173. doi 10.1007/s00220-014-2261-0. Also preprint arXiv math.1302.3647, also American Institute of Mathematics preprint 2013-20.
Discrete entropy of generalized Jacobi polynomials
A. Martínez-Finkelshtein, P. Nevai, A. Peña, J. Math. Annal. Appl. 431 (2015), 99-110. Also preprint arXiv math.1410.2286.
Strong asymptotics for the Pollaczek multiple orthogonal polynomials
A. Aptekarev, G. López-Lagomasino, A. Martínez-Finkelshtein, Doklady Akademii Nauk, 2015, Vol. 465, No. 4, pp. 393–397; English transl. in Doklady Mathematics, 2015, Vol. 92, No. 3, pp. 709–713.
Quadratic differentials and asymptotics of Laguerre polynomials with varying complex parameters
M. J. Atia, A. Martinez-Finkelshtein, P. Martinez-Gonzalez, F. Thabet, J. Math. Anal. Appl. 416 (2014), 52-80. Also preprint arXiv math.1311.0372.
Computational aspects of the through-focus characteristics of a human eye
D. Ramos-López, A. Martínez-Finkelshtein, and D. Robert Iskander, J. Optical Soc. of America A 31(7) (2014), 1408-1415.
A differential equation for Hermite-Padé polynomials
A. Martinez-Finkelshtein, E. A. Rakhmanov, S. P. Suetin, Uspekhi Mat. Nauk, 68:1(409) (2013), 197-198 (in Russian). English transl. in Russian Math. Surveys 68:1, (2013), 183-184.
Screening subclinical keratoconus with Placido-based corneal indices
D. Ramos-López, A. Martínez-Finkelshtein, G. M. Castro-Luna, N. Burguera-Gimenez, A. Vega-Estrada, D. Piñero, J. L. Alió, Optometry and Vision Science 90, No. 4, 2013, pp. 335-343.
Heine, Hilbert, Pade, Riemann, and Stieltjes: a John Nuttall's work 25 years later
A. Martinez-Finkelshtein, E. A. Rakhmanov, S. P. Suetin, Contemporary Mathematics 578 (2012), 165-193, DOI http://dx.doi.org/10.1090/conm/578/11474. Also preprint arXiv:1111.6139.
Method of inner variations and existence of S-compacts
V. I. Buslaev, A. Martínez-Finkelshtein, S. P. Suetin, Trudy MIAN 279 (2012), 31-58 (in Russian). English transl. in: Proc. Steklov Inst. Math. 279 (2012), 25-51.
Asymptotics of the L^2 Norm of Derivatives of OPUC
A. Martínez-Finkelshtein, B. Simon, , J. Approx. Theory 163 , 747-778 (2011). Also preprint arXiv:1006.0900 [math.CA ]. arXiv:1006.0900
Critical measures, quadratic differentials, and weak limits of zeros of Stieltjes polynomials
A. Martinez-Finkelshtein, E. A. Rakhmanov, Comm. Math. Physics 302 , 53-111 (2011). Also preprint arXiv:0902.0193 [math.CA ]. arXiv:0902.0193 [math.CA
Asymptotics of orthogonal polynomials for a weight with a jump on [-1,1]
A. Foulquie Moreno, A. Martínez-Finkelshtein, V.L. Sousa, Constructive Approximation 33 , 219-263 (2011). Also preprint arXiv:0904.2514 [math.CA ]. arXiv:0904.2514 [math.CA
Variation of the equilibrium measure and the S-property of stationary compact sets
A. Martínez-Finkelshtein, E. A. Rakhmanov, S. P. Suetin, Uspekhi Mat. Nauk, 66 :1(397) (2011), 183–184 (in Russian). English transl. in : Russian Mathematical Surveys, 2011, 66:1, 176-178.
Adaptive cornea modeling from keratometric data
A. Martínez-Finkelshtein, D. Ramos-López, G. M. Castro-Luna, J. L. Alió, Investigative Ophthalmology and Visual Science 52 (8) (2011), 4963-4970. Also preprint arXiv:1009.1244 [math.CA] . arXiv:1009.1244 [math.CA]
Book reviews
A. Martinez-Finkelshtein (ed.), . Journal of Approximation Theory 163 (2011), 1029-1047.
Placido-based indices of corneal irregularity
D. Ramos-López, A. Martínez-Finkelshtein, G. M. Castro-Luna, D. Piñero, J. L. Alió, Optometry and Vision Science 88 (10) (2011), 1220-1231 .
Non-intersecting squared Bessel paths: critical time and double scaling limit
A.B.J. Kuijlaars, A. Martinez-Finkelshtein, F. Wielonsky, Comm. Math. Physics. 308 (2011), 227-279. Also preprint arXiv:1011.1278 [math.CA ]. arXiv:1011.1278 [math.CA
Properties of matrix orthogonal polynomials via their Riemann-Hilbert characterization
F. Alberto Grünbaum, Manuel D. de la Iglesia, Andrei Martinez-Finkelshtein, SIGMA 7 (2011), 098, 31 pages . Also preprint arXiv:1106.1307 [math.CA ]. arXiv:1106.1307 [math.CA
Padé approximants, continued fractions, and orthogonal polynomials
A. I. Aptekarev, V. I. Buslaev, A. Martínez-Finkelshtein, S. P. Suetin, Uspehi Mat. Nauk 66 (6), (2011), 37-122 (in Russian). English transl. in Russian Math. Surveys 66 :6 1049–1131 (2011). Padé approximants, continued fractions, and orthogonal polynomials
Variation of the equilibrium measure and the S-property of stationary compact sets
A. Martínez-Finkelshtein, E. A. Rakhmanov, S. P. Suetin, Mat. Sbornik, 202 :12 (2011), 113–136 (in Russian). English transl. in Sbornik: Mathematics 202 :12 1831–1852(2011).
Asymptotics of orthogonal polynomial's entropy
A.I. Aptekarev, J.S. Dehesa, A. Martinez-Finkelshtein, Journal of Comput. Applied Math. 233 , 1355-1365 (2010).
Guillermo López Lagomasino: mathematical life
F. Marcellán and A. Martínez-Finkelshtein, Contemporary Mathematics 507, 1-24, 2010.
On asymptotic behavior of Heine-Stieltjes and Van Vleck polynomials
A. Martinez-Finkelshtein, E. A. Rakhmanov, Contemporary Mathematics 507 , 209-232 (2010). Also preprint arXiv:0903.2614 [math.CA ]. arXiv:0903.2614 [math.CA
Book reviews
A. Martinez-Finkelshtein (ed.), . Journal of Approximation Theory 162 (2010), 221-238, DOI 10.1016/j.jat.2008.11.004.
On a conjecture of A. Magnus concerning the asymptotic behavior of the recurrence coefficients of the generalized Jacobi polynomials
A. Foulquie Moreno, A. Martínez-Finkelshtein, V.L. Sousa, Journal of Approximation Theory 162 (2010) 807–831. Also preprint arXiv:0905.2753 [math.CA ]. arXiv:0905.2753 [math.CA
Book reviews
A. Martinez-Finkelshtein (ed.), . Journal of Approximation Theory 162 (2010), 869–889, DOI:10.1016/j.jat.2010.02.001.
Quantum expectation values of D-dimensional Rydberg hydrogenic states by use of Laguerre and Gegenbauer asymptotics
A.I. Aptekarev, J S Dehesa, A Martínez-Finkelshtein, R.J. Yáñez, J. Phys. A: Math. Theor. 43 (2010) 145204 (10pp).
Information theory of D-dimensional hydrogenic systems. Application to circular and Rydberg states
J. S. Dehesa, S. López-Rosa, A. Martínez-Finkelshtein, R. J. Yáñez, International Journal of Quantum Chemistry 110 (8), 1529-1548 (July 2010).

Non-intersecting squared Bessel paths and multiple orthogonal polynomials for modified Bessel weights
A.B.J. Kuijlaars, A. Martinez-Finkelshtein, F. Wielonsky, Communications in Mathematical Physics 286, 217–275 (2009), doi 10.1007/s00220-008-0652-9. Also preprint arXiv:0712.1333 [math.CA ]. arXiv:0712.1333 [math.CA
Book reviews
A. Martinez-Finkelshtein (ed.), . Journal of Approximation Theory 156 (2009), 95-115, DOI 10.1016/j.jat.2008.11.012.
Discrete entropies of orthogonal polynomials
A.I. Aptekarev, J.S. Dehesa, A. Martinez-Finkelshtein, R. Yañez, Constructive Approximation 30 (2009): 93-119, DOI 10.1007/s00365-008-9028-9. Also preprint arXiv:0710.2134 [math.CA ]. arXiv:0710.2134 [math.CA
Narayana numbers and Schur-Szegö composition.
V. P. Kostov, A. Martínez-Finkelshtein, B. Z. Shapiro, Journal of Approximation Theory 161, 464-476 (2009).
Comparative analysis of some modal reconstruction methods of the shape of the cornea from the corneal elevation data
A. Martínez-Finkelshtein, A. M. Delgado, G. M. Castro, A. Zarzo, J. L. Alió, , Investigative Ophthalmology and Visual Science 50 (12), 5639-5645 (2009).
Strong Asymptotics for Sobolev orthogonal polynomials in the complex plane.
G. Lopez Lagomasino, A. Martinez-Finkelshtein, I. Perez-Izquierdo, and H. Pijeira-Cabrera, Journal of Mathematical Analysis and Application s 340 , 521-535 (2008).
Book reviews
A. Martinez-Finkelshtein (ed.), . Journal of Approximation Theory 154 (2008), pp. 59-75.
Pólya frequency sequences and real zeros of some 3F2 polynomials
K. Driver, K. Jordaan, and A. Martínez-Finkelshtein, Journal of Mathematical Analysis and Applications 332 , 1045-1055 (2007).
Shannon entropy of symmetric Pollaczek polynomials
A. Martinez-Finkelshtein, J. F. Sanchez-Lara, Journal of Approximation Theory 145, 55-80 (2007). Also preprint math.CA/0504250 . math.CA/0504250
Electrostatic models for zeros of polynomials: old, new, and some open problems.
F. Marcellán, A. Martínez-Finkelshtein, P. Martínez-González, J. Comput. Appl. Math. 207 (2) , 258-272 (2007). Also preprint math.CA/0512293 . math.CA/0512293
Information-theoretic measures for Morse and Pöschl-Teller potentials
J. S. Dehesa, A. Martínez-Finkelshtein, V. N. Sorokin, Molecular Physics 104 (4), 613-622, 2006.
Szegö orthogonal polynomials with respect to an analytic weight: canonical representation and strong asymptotics
A. Martinez-Finkelshtein, K. T.-R. McLaughlin, and E. B. Saff, Constructive Approximation 24 (3), 319-363 (2006) ( DOI: 10.1007/s00365-005-0617-6 ). Also preprint math.CA/0502300. 10.1007/s00365-005-0617-6 math.CA/0502300
Equilibrium Problems Potential Theory in the Complex Plane
A. Martinez-Finkelshtein, En "Orthogonal Polynomials and Special Functions", Lecture Notes Math. 1883, Van Assche, Walter; Marcellán, Francisco (Eds.), 79-117 (2006). "Orthogonal Polynomials and Special Functions"
On extensions of a theorem of Baxter
J. S. Geronimo, A. Martinez-Finkelshtein, . J. Approx. Theory 139 (1-2), 214-222 (2006). Also preprint math.CA/0508224. math.CA/0508224
Asymptotics of orthogonal polynomials with respect to an analytic weight with algebraic singularities on the circle
A. Martinez-Finkelshtein, K. T.-R. McLaughlin, and E. B. Saff, Internat. Math. Research Notices (2006), doi:10.1155/IMRN/2006/91426. Also preprint math.CA/0605715. math.CA/0605715
Szegö polynomials: a view from the Riemann-Hilbert window
A. Martinez-Finkelshtein, . Electronic Trans. Numer. Anal. 25 , 369-392 (2006). Also preprint math.CA/0508117. Electronic Trans. Numer. Anal. math.CA/0508117
Open problems in constructive function theory
L. Baratchart, A. Martinez-Finkelshtein, D. Jimenez, D. S. Lubinsky, H. N. Mhaskar, I. Pritsker, M. Putinar, N. Stylianopoulos, V. Totik, P. Varju, and Y. Xu. Electronic Trans. Numer. Anal. 25 , 511-525 (2006). Electronic Trans. Numer. Anal.
Orthogonality of Jacobi polynomials with general parameters
A.B.J. Kuijlaars, A. Martinez-Finkelshtein, R. Orive, Electronic Trans. Numer. Anal. Vol. 19 , 1-17 (2005) . Also preprint math.CA/0301037. math.CA/0301037
Asymptotics of polynomial solutions of a class of generalized Lamé differential equations
A. Martinez-Finkelshtein, P. Martínez-González, R. Orive, Electronic Trans. Numer. Anal., Vol. 19 , 18-28 (2005).
Riemann-Hilbert analysis for Jacobi polynomials orthogonal on a single contour
A. Martinez-Finkelshtein, R. Orive, J. Approx. Theory Vol. 134 , 137-17 (2005). Also preprint math.CA/04103205. math.CA/04103205
Las ganancias del comercio y el intercambio desigual en los modelos del comercio internacional,
F. Martínez Soler, A. Martinez-Finkelshtein, Revista de Economía Crítica, Vol. 4, 115-140 (2005).
Asymptotics for minimal discrete Riesz energy on curves in R^d
A. Martínez-Finkelshtein, V. Maymeskul, E. A. Rakhmanov, E. B. Saff, Canadian Journal of Mathematics Vol. 56, No. 3, 529–552 (2004), MR number 2057285 (2005a:31010).
Asymptotic upper bounds for the entropy of orthogonal polynomials in the Szegö class
B. Beckermann, A. Martinez-Finkelshtein, E.A. Rakhmanov, and F. Wielonsky, J. Math. Physics 45 (11), 4239-4254 (2004), MR number 2098132 (2005f:42052) . Also preprint math.CA/0311055 . math.CA/0311055
Computation of the entropy of polynomials orthogonal on an interval
V. Buyarov, J. S. Dehesa, A. Martinez-Finkelshtein, J. Sanchez-Lara, SIAM J. Scientific Computing 26 (2), 488-509 (2004). Also preprint math.NA/0310238. math.NA/0310238
Strong asymptotics for Jacobi polynomials with varying nonstandard parameters
A.B.J. Kuijlaars, A. Martinez-Finkelshtein, J. d'Analyse Mathematique 94 , 195-234 (2004). Also preprint math.CA/0309443. math.CA/0309443
Asymptotics of information entropies of some Toda-like potentials
J. S. Dehesa, A. Martínez-Finkelshtein, V. N. Sorokin, J. Math. Phys. Vol. 44, No. 1, 36-47 (2003). MR number 1946690 (2003i:81057).
El Análisis Numérico en los últimos 25 años
A. Martínez-Finkelshtein, , Revista LLULL 26 , 919-928 (2003).
WKB approach to zero distribution of solutions of linear second order differential equations
A. Martínez-Finkelshtein, P. Martínez-González, A. Zarzo, , J. Comput. Appl. Math. 145 , 167-182 (2002). MR number 1914357 (2003e:34102).
Asymptotic properties of Heine-Stieltjes and Van Vleck polynomials
A. Martínez-Finkelshtein, E. B. Saff, , J. Approx. Theory 118 , 131-151 (2002). MR number 1928260 (2003j:33031).
Quantum information entropies for highly excited states of single-particle systems with power-type potentials
J. S. Dehesa, A. Martínez-Finkelshtein, V. N. Sorokin, Phys. Review A, Vol. 66, 062190, 1-7 (2002).
Short-wave asymptotics of the information entropy of a circular membrane
J. S. Dehesa, A. Martínez-Finkelshtein, V. N. Sorokin, , Int. J. Bifurcation and Chaos, Vol. 12, No. 11, 2387-2392 (2002). MR number 1955995 (2004a:82050).
Analytic aspects of Sobolev orthogonality revisited
A. Martínez-Finkelshtein, , J. Comput. and Appl. Math. 127 (1-2), 255-266 (2001), MR number 1808577 (2002d:33018) .
k-coherence of measures with non-classical weights
F. Marcellán, A. Martínez-Finkelshtein, J. J.Moreno-Balcázar, In: Margarita Mathematica en honor de José Javier Guadalupe Hernández, Chicho. Serv. Publ. Universidad de La Rioja, 2001, pag. 77-83. MR number 1882617 (2003b:42042).
On asymptotic zero distribution of Laguerre and generalized Bessel polynomials with varying parameters
A. Martínez-Finkelshtein, P. Martínez-González, R. Orive, J. Comput. Appl. Math. 133 , 1-2, 477-487 (2001).
Quantum information entropies and orthogonal polynomials
J. S. Dehesa, A. Martínez-Finkelshtein, J. Sánchez-Ruiz, J. Comput. Appl. Math. 133 , 1-2, 23-46 (2001).
Bernstein-Szegö's theorem for Sobolev orthogonal polynomials
A. Martínez-Finkelshtein, Constr. Approx. 16 , (2000), 73-84.
Information entropy of Gegenbauer polynomials
V. S. Buyarov, P. López-Artés, A. Martínez-Finkelshtein, and W. Van Assche, J. of Physics A 33 , 37 (2000), 6549-6560.

Asymptotic Properties of Balanced Extremal Sobolev Polynomials: Coherent Case,
M. Alfaro, A. Martínez-Finkelshtein, M.Rezola, J. Approx. Theory 100 (1999), 44-59.
Strong Asymptotics for Sobolev Orthogonal Polynomials
A. Martínez-Finkelshtein, H. Pijeira Cabrera, J. d'Analyse Math. 78 (1999), 143-156.
General linearization formulas for products of continuous hypergeometric-type polynomials,
P. L. Artés, J. S. Dehesa, A. Martínez-Finkelshtein, J. Sánchez-Ruiz, J. of Physics A 32 , 42 (1999), 7345-7366.
Analytic properties of non-diagonal Jacobi-Sobolev orthogonal polynomials
J.J. Moreno-Balcázar, A. Martínez-Finkelshtein, J. Comput. and Appl. Math. 105 , 1-2(1999), 393-401.
Asymptotics of the information entropy for Jacobi and Laguerre polynomials with varying weights
J. S. Dehesa, V. S. Buyarov, A. Martínez-Finkelshtein, E. B. Saff, J. Approx. Theory 99 (1999), 153-166, Article jath.1988.3315.
Finite-dimensional approximations of the resolvent of an infinite band matrix and continued fractions
D. Barrios, G. López, A. Martínez, E. Torrano, Matem. Sbornik 190, No. 4 (1999), 23-42. English transl. in Sbornik: Mathematics 190, No. 4 (1999), 501-519
Linearization and connection coefficients for hypergeometric-type polynomials
P. L. Artés, J. S. Dehesa, A. Martínez-Finkelshtein, J. Sánchez-Ruiz, Comput. and Appl. Math. 99 (1998), 15-26.
Asymptotic properties of Sobolev orthogonal polynomials
A. Martínez-Finkelshtein, Comput. and Appl. Math. 99 (1998), 491-510.
Asymptotics of Sobolev orthogonal polynomials for coherent pairs of measures
A. Martínez-Finkelshtein, J.J. Moreno-Balcázar, T. Pérez y M. Piñar, J. Approx. Theory 92 (2), 280-293 (1998).
On the domain of convergence and poles of complex J-fractions
D. Barrios, G. López, A. Martínez, E. Torrano, J. Approx. Theory 93 (2), 177-200 (1998).
Strong asymptotics for Gegenbauer-Sobolev orthogonal polynomials
A. Martínez-Finkelshtein, J.J. Moreno-Balcázar y H. Pijeira-Cabrera, J. Comput. and Appl. Math. 81 (1997), 211-216.
Asymptotics of Sobolev orthogonal polynomials for symmetrically coherent pairs of measures with compact support
F. Marcellán, A. Martínez-Finkelshtein, J.J. Moreno-Balcázar, J. Comput. and Appl. Math. 81 (1997), 217-227.
Asymptotics of Sobolev orthogonal polynomials for Jacobi weights
A. Martínez-Finkelshtein, J.J. Moreno-Balcázar, Methods and Applications of Analysis 4 (4), 430-437 (1997).
Zero asymptotics of Laurent orthogonal polynomials
M. Bello, A. Martínez, J. Approx. Theory, 85 , No. 3 (1996), 324-342.
Rate of convergence of two-point Pade approximants and logarithmic asymptotics of Laurent-type orthogonal polynomials
G. López Lagomasino, A. Martínez Finkelshtein, Constr. Approx., 11, (1995), 255-286.
Two approaches to the zero asymptotics of a class of hypergeometric-type polynomials
A. Martínez, A. Zarzo, R. Yañez, Matem. Sbornik, 185 (12), (1994), 65 -78; English Trans. in Russian Acad. Sci. Sb. Math., Vol 83 (1995), No. 2, 483-493.
The Quantum Relativistic Harmonic Oscilator: Spectrum of Zeros of its Wave Functions
A. Zarzo, A. Martínez, J. Math. Physics, 34 (7), (1993), 2926 - 2935.

In Conference proceedings

Varying orthogonality for a class of hypergeometric-type polynomials
A. Martínez, A. Zarzo, Approximation and Optimization in the Caribbean II, M. Florenzano, J. Guddat, M. Jiménez, H. Th. Jongen, G. López, F. Marcellán, (eds.), Peter Lang Series on Approximation and Optimization, Vol. 8, 1995, 540-554.
Asymptotic properties of some Laurent-type polynomials
A. Martínez, Approximation and Optimization in the Caribbean II, M. Florenzano, J. Guddat, M. Jiménez, H. Th. Jongen, G. López, F. Marcellán, (eds.), Peter Lang Series on Approximation and Optimization, Vol. 8, 1995, 529-539.
Trajectories of quadratic differentials and approximations of exponents on the semiaxis
A. Martínez Finkelshtein, In "Complex Methods in Approximation Theory", A. Martínez Finkelshtein, F. Marcellán, J.J. Moreno, eds., Universidad de Almería (1997), pag. 69-84.
Asymptotics for Gegenbauer-type polynomials
A. Martínez Finkelshtein, J.J. Moreno-Balcázar y H. Pijeira-Cabrera, In "Complex Methods in Approximation Theory", A. Martínez Finkelshtein, F. Marcellán, J.J. Moreno, eds., Universidad de Almería (1997), pag. 85-91.
Zero distribution of solutions of linear second order differential equations
A. Martínez Finkelshtein, A. Zarzo, In "Complex Methods in Approximation Theory", A. Martínez Finkelshtein, F. Marcellán, J.J. Moreno, eds., Universidad de Almería (1997), pag. 93-108.
Zeros of Jacobi Polynomials with Varying Non-Classical Parameters
A. Martínez-Finkelshtein, P. Martínez-González, R. Orive, Proceedings of the International Workshop on Special Functions: Asymptotics, Harmonic Analysis, and Mathematical Physics. City University of Hong Kong, June 21-25, 1999. World Scientific (2000), 98-113.

Books and Edited Volumes

"Complex Methods in Approximation Theory",
Universidad de Almería, ISBN 84-8240-046-0, 1997.

"Métodos Numéricos: Aproximación en R",
Universidad de Almería, ISBN 84-8240-259-5, 1999.

"Métodos Numéricos: Resolución de ecuaciones,
Universidad de Almería, ISBN 84-8240-471-7, 2001.

"From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory", Operator Theory: Advances and Applications 285, F. Gesztesy, A. Martinez-Finkelshtein (eds.),
https://doi.org/10.1007/978-3-030-75425-9_12.

“Developments in Orthogonal Polynomials”, A. Barhoumi, R. Gharakhloo, A. Martínez-Finkelshtein (editors),
Contemporary Mathematics (Volume 822), AMS, 2025. ISBN 978-1-47047496-6.