"Special functions and Approximation Theory: applications in Science and Technology" (SFAT-ST)
Research subproject MTM2011-28952-C02-01 from the Ministry of Science and Innovation of Spain and the European Regional Development Fund (ERDF)

Coordinator: Andrei Martínez-Finkelshtein

List of publications:

Preprints and papers in press:

1. M.J. Cantero, L. Moral, L. Velázquez, Linear spectral transformations of Carathéodory functions, preprint arXiv math.1302.2007.
2. M.J. Cantero, A. Iserles, Orthogonal polynomials on the unit circle and functional-differential equations. DAMTP Tech. Rep. 2011/NA08.
3. M.J. Cantero, A. Iserles, From orthogonal polynomials on the unit circle to functional equations via generating functions, DAMPT NA2013/06 Technical Report. Transactions of the American Mathematical Society, available on-line, doi 10.1090/tran/6454.
4. A. Aptekarev, G. López-Lagomasino, A. Martínez-Finkelshtein, On Nikishin systems with discrete components and weak asymptotics of multiple orthogonal polynomials, preprint arXiv math.1403.3729.
5. A. Aptekarev, G. López-Lagomasino, A. Martínez-Finkelshtein, Strong asymptotics for the Pollaczek multiple orthogonal polynomials ensembles, preprint arXiv math.1410.1261. 
6. A. Martínez-Finkelshtein, D. Ramos-López, and D. Robert Iskander, Computation of 2D Fourier transforms and diffraction integrals using Gaussian radial basis functions, preprint arXiv math.1506.01670.
   
7. A. Martínez-Finkelshtein, E. A. Rakhmanov, S. P. Suetin, Asymptotics of type I Hermite–Padé polynomials for semiclassical functions, preprint arXiv math.1502.01202.
8. A. Martínez-Finkelshtein, P. Martínez-González, F. Thabet, Trajectories of quadratic differentials for Jacobi polynomials with complex parameters, to appear in Comput. Methods and Function Theory. Also preprint arXiv math.1506.03434.
9. A. Martínez-Finkelshtein, G. Silva, Critical measures for vector energy: global structure of trajectories of quadratic differentials, preprint arxiv math.1509.06704.
10. A. Martínez-Finkelshtein, A. Sri Ranga, Daniel O. Veronese, Extreme zeros in a sequence of para-orthogonal polynomials and bounds for the support of the measure, preprint arXiv math.1505.07788.
11. A. Martinez-Finkelshtein, E. A. Rakhmanov, Do orthogonal polynomials dream of symmetric curves?, preprint
    arXiv math.1511.09175.
12. M.J. Cantero, F. Marcellán, L. Moral, L. Velázquez, Darboux transformations for CMV matrices, preprint arxiv:1503.05003.
13. C. Cedzich, F.A. Grünbaum, L. Velázquez, A.H. Werner, R.F. Werner, A quantum dynamical approach to matrix Khrushchev’s formulas,  Comm. Pure Appl. Math. (in press). Also preprint arXiv:1405.0985.
14. C.F. Bracciali, J.J. Moreno-Balcázar, Mehler-Heine Asymptotics of a Class of Generalized Hypergeometric Polynomials, Oberwolfach Preprints 23, 2013.
15. C. Cedzich, F.A. Grünbaum, L. Velázquez, A.H. Werner, R.F. Werner, Bulk-edge correspondence of one-dimensional quantum walks, preprint arXiv:1502.02592 [quant-ph].
16. A. Deaño, A.B.J. Kuijlaars and P. Román, Asymptotic behavior and zero distribution of polynomials orthogonal with respect to Bessel functions, to appear in Constructive Approximation. Preprint arXiv:1406.0969.
17. J.F. Mañas-Mañas , F. Marcellán, J.J. Moreno Balcázar, Asymptotic behavior of varying discrete Jacobi-Sobolev orthogonal polynomials, Journal of Computational and Applied Mathematics, accepted.

2016:

• D. Ramos-López, M. A. Sánchez-Granero, M. Fernández-Martínez, and A. Martínez-Finkelshtein, Optimal sampling patterns for Zernike polynomials, Applied Mathematics and Computation 274 (2016) 247-257. Also preprint arXiv math.1511.00449.

2015:

• M. Alfaro, J.J. Moreno-Balcázar, A. Peña, M.L. Rezola, Asymptotic formulae for generalized Freud polynomials,  Journal of Mathematical Analysis and Applications 421, 474-488, 2015.
• C.F. Bracciali, J.J. Moreno-Balcázar, On the zeros of a class of generalized hypergeometric polynomials, Applied Mathematics and Computation 253, 151-158, 2015. 
• J. J. Moreno-Balcázar, Δ-Meixner-Sobolev orthogonal polynomials: Mehler-Heine type formula and zeros, Journal of Computational and Applied Mathematics 284, 228-234, 2015.
• A. Bultheel, M.J. Cantero, R. Cruz-Barroso, Matrix methods for quadrature formulas on the unit circle. A survey, J. Comput. Appl. Math. 284 (2015) 78–100.
• A.B.J. Kuijlaars, G. Silva, S-curves in polynomial external fields, J. Approx. Theory 191 (2015), 1-37. Also preprint arXiv:1311.7026.
• A.B.J. Kuijlaars, A. López, A vector equilibrium problem for the normal matrix model, and multiple orthogonal polynomials on a star, Nonlinearity 28 (2015), 347--406. Also preprint arXiv:1401.2419.
• A. Martínez-Finkelshtein, E. A. Rakhmanov, R. Orive, Phase transitions and equilibrium measures in random matrix models, Comm. Math. Physics 333 (3) (2015), 1109-1173. doi 10.1007/s00220-014-2261-0. Also preprint arXiv math.1302.3647, as well as American Institute of Mathematics preprint 2013-20. 
• A. Martínez-Finkelshtein, P. Nevai, A. Peña, Discrete entropy of generalized Jacobi polynomials, to appear in the J. Math. Annal. Appl. 431 (2015), 99-110. Also preprint arXiv math.1410.2286.
• A. Aptekarev, G. López-Lagomasino, A. Martínez-Finkelshtein, Strong asymptotics for the Pollaczek multiple orthogonal polynomials, Doklady Akademii Nauk, 2015, Vol. 465, No. 4, pp. 393–397; English transl. in Doklady Mathematics, 2015, Vol. 92, No. 3, pp. 709–713.

2014:

• A.B.J. Kuijlaars, The tacnode Riemann-Hilbert problem, Constr. Approx. 39 (2014), 197--222.
• M. J. Atia, A. Martinez-Finkelshtein, P. Martinez-Gonzalez, F. Thabet, Quadratic differentials and asymptotics of Laguerre polynomials with varying complex parameters, J. Math. Anal. Appl. 416 (2014), 52-80. Also preprint arXiv math.1311.0372.
• D. Ramos-López, A. Martínez-Finkelshtein, and D. Robert Iskander, Computational aspects of the through-focus characteristics of a human eye, J. Optical Soc. of America A 31(7) (2014), 1408-1415.
• J. Bourgain, F.A. Grünbaum, L. Velázquez, J. Wilkening, Quantum Recurrence of a Subspace and Operator-Valued Schur Functions,
  Commun. Math. Phys. 329 (2014) 1031-1067. Also preprint arxiv:1302.7286 [quant-ph].
• E.N. Petropoulou, L. Velázquez, Self-adjointness of unbounded tridiagonal operators and spectra of their finite truncations, J. Math. Anal. Appl. 420 (2014) 852-872. Also preprint arXiv:1402.1334 [math.FA].
• M. Duits, A.B.J. Kuijlaars, and M.Y. Mo, Asymptotic analysis of the two matrix model with a quartic potential, in "Random Matrix Theory, Interacting Particle Systems, and Integrable Systems" (P. Deift and P. Forrester, eds.), Mathematical Sciences Research Institute Publications (No. 65), Cambridge University Press, New York, 2014, pp. 147--162. Also preprint arXiv1210.0097.
• A.B.J. Kuijlaars, D. Stivigny, Singular values of products of random matrices and polynomial ensembles, Random Matrices: Theory and Applications 3 (2014), article nr. 1450011, 22 pp. (arXiv:1404.5802).
• A.B.J. Kuijlaars, L. Zhang, Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits, Comm. Math. Phys. 332 (2014), 759-781. Also preprint arXiv:1308.1003.
• D. Huybrechs, A.B.J. Kuijlaars, N. Lejon, Zero distribution of complex orthogonal polynomials with respect to exponential weights, J. Approx. Theory. 184 (2014), 28-54. Also preprint arXiv:1312.4376.

2013:

• D. Ramos-López, A. Martínez-Finkelshtein, G. M. Castro-Luna, N. Burguera-Gimenez, A. Vega-Estrada, D. Piñero, J. L. Alió, Screening subclinical keratoconus with Placido-based corneal indices. Optometry and Vision Science 90, No. 4, 2013, pp. 335-343. 
• A. Martinez-Finkelshtein, E. A. Rakhmanov, S. P. Suetin, A differential equation for Hermite-Padé polynomials, Uspekhi Mat. Nauk, 68:1(409) (2013), 197-198 (en ruso). Traducción al inglés en Russian Math. Surveys 68:1, (2013), 183-184.
• F.A. Grünbaum, L. Velázquez, A.H. Werner, R.F. Werner, Recurrence for discrete time unitary evolutions, Communications in Mathematical Physics, 320 (2) (2013), 543-569. Also preprint arXiv:1202.3903 [quant-ph].
• M.J. Cantero, A. Iserles, On expansions in orthogonal polynomials, Adv. Comp. Maths. 38 (2013), no. 1, 35–61. DAMTP Tech. Rep. 2011/NA05.
• A. Hardy and A.B.J. Kuijlaars, Large deviations for a non-centered Wishart matrix,  Random Matrices: Theory and Applications 2 (2013), 1250016. Also preprint arXiv:1204.6261.
• L. Castaño-García, J.J. Moreno-Balcázar, Zeros of varying Laguerre-Krall orthogonal polynomials, Proceedings of the American Mathematical Society, 141(6), 2051-2060, 2013.
• B. Xh. Fejzullahu, F. Marcellán, J.J. Moreno-Balcázar, Jacobi-Sobolev orthogonal polynomials: asymptotics and a Cohen type inequality, Journal of Approximation Theory, 170, 78-93, 2013.
• J.F. Mañas-Mañas, F. Marcellán, J.J. Moreno-Balcázar, Varying discrete Laguerre-Sobolev  orthogonal polynomials: asymptotic behavior and zeros. Applied Mathematics and Computation,  222, 612-618, 2013.
• D. Canca, A. Zarzo,  E. Algaba,  E. Barrena, Macroscopic attraction-based simulation of pedestrian mobility: A dynamic individual route-choice approach. European Journal of Operational Research (Eur. J. Oper. Res.) 231 (2) (2013) 428-444.
• D. Canca, A. Zarzo, P. L. Gonzalez-Rodriguez, E. Barrena, E. Algaba, A methodology for schedule-based paths recommendation in multimodal public transportation networks. Journal of Advanced Transportation (J. Adv. Transport.) 47 (3) (2013) 319–335.
• Canca, E. Barrena, E. Algaba, A. Zarzo, Design and analysis of demand-adapted railway timetables, Journal of Advanced Transportation (J. Adv. Transport.) 48 (2) (2014) 119–137.
• Canca, E. Algaba, E. Barrena, A. Zarzo, Railway rapid transit timetables with variable and elastic demand, Procedia - Social and Behavioral Sciences, 111 (2014) 538-548.
• P. Sanchez-Moreno, J.S. Dehesa, A. Zarzo, Renyi entropies, Lq norms and linearization of powers of hypergeometric orthogonal polynomials by means of multivariate special functions. Applied Mathematics and Computation (Appl. Math. Comput.) 223 (2013) 25-33.

2012:

1. A. Martinez-Finkelshtein, E. A. Rakhmanov, S. P. Suetin, Heine, Hilbert, Pade, Riemann, and Stieltjes: a John Nuttall's work 25 years later, Contemporary Mathematics 578 (2012), 165-193, DOI http://dx.doi.org/10.1090/conm/578/11474. Also preprint arXiv:1111.6139.
2. V. I. Buslaev, A. Martínez-Finkelshtein, S. P. Suetin, Method of inner variations and existence of S-compacts, Trudy MIAN 279 (2012), 31-58 (in Russian). English translation: Proc. Steklov Inst. Math. 279 (2012), 25-51.
3. L. Castaño-García, J.J. Moreno-Balcázar, Varying Sobolev type orthogonal polynomials: the Laguerre case, Jaen Journal of Approximation, 4(2) (2012), 85–99.
4. J.J. Moreno-Balcázar, Varying Jacobi-Krall orthogonal polynomials: local asymptotic behaviour and zeros, The Ramanujan Journal, 28, 79-88, 2012.
5. J.F. Mañas-Mañas, F. Marcellán, J.J. Moreno-Balcázar, Local asymptotics for a family of Sobolev type orthogonal polynomials, Proceedings of the 12th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2012, pp 785-791. ISBN:978-84-615-5392-1.
6. M.J. Cantero, F.A. Günbaum, L. Moral, L. Velázquez, One-dimensional quantum walks with one defect, Reviews in Mathematical Physics 24 (2012), 1250002 (52 pp).
7. M.J. Cantero, F.A. Grünbaum, L. Moral, L. Velázquez, The CGMV method for quantum walks, Quantum Information Processing 11 (2012), 1149–1192.
8. M.J. Cantero, L. Moral, L. Velázquez, Spectral transformations of hermitian linear functionals, Contemporary Mathematics 578 (2012), 63–82, DOI http://dx.doi.org/10.1090/conm/578/11474.
9. B. Olmos, R. González-Férez, I. Lesanovsky, L. Velázquez, Universal time evolution of a Rydberg lattice gas with perfect blockade, J. Phys. A: Math. Theor. 45 (2012), 325301 (25 pp).
10. F.A. Grünbaum, L. Velázquez, The quantum walk of F. Riesz, in F. Cucker, T. Krick, A. Pinkus, A. Szanto (eds.) Proceedings of FoCAM2011, London Mathematical Society Lecture Notes Series, 403, pp. 93–112, Nov. 2012.
    
11. A. Hardy, A.B.J. Kuijlaars, Weakly admissible vector equilibrium problems, J. Approx. Theory 164 (2012), 854-868. (also arXiv:1110.6800).
12. P. Sánchez-Moreno, A. Zarzo and J.S. Dehesa, Jensen divergence based on Fisher’s information, J. Phys. A: Math. Theor. 45 (2012) 125305 (14pp), doi:10.1088/1751-8113/45/12/125305.
13. A. Martínez-Finkelshtein, E. A. Rakhmanov, S. P. Suetin, A differential equation for Hermite-Padé polynomials, Uspekhi Mat. Nauk, 68:1(409) (2013), 197-198.
14. M.J. Cantero, A. Iserles, On rapid computation of expansions in ultraspherical polynomials, SIAM J. Numer. Anal. 50 (2012), no. 1, 307–327.
15. M.J. Cantero, A. Iserles, On a curious q-hypergeometric identity, Nonlinear analysis, 121–126, Springer Optim. Appl., 68, Springer, New York, 2012. DAMTP Tech. Rep. 2011/NA09.