Research

I do research in Analysis. My current research interests are concentrated in the following areas:

  • Multiorthogonal polynomials
  • Minimal energy problems and Potential Theory
  • Random matrices and random polynomials

A list of my publications and preprints is given here:

  1. A. López-García and E. Miña-Díaz, Asymptotics of the optimal values of potentials generated by greedy energy sequences on the unit circle, J. Math. Anal. Appl. 538 (2024) 128401, 20 pp. [arXiv]
  2. J. Kim, A. López-García, and V.A. Prokhorov, Matrix continued fractions associated with lattice paths, resolvents of difference operators, and random polynomials, accepted in Constructive Approximation, arXiv:2307.02619. [arXiv]
  3. A. López-García and A. Tovbis, Non-standard Green energy problems in the complex plane, Anal. Math. Phys. 13, 77 (2023). [arXiv]
  4. A. López-García and V.A. Prokhorov, Lattice paths, vector continued fractions, and resolvents of banded Hessenberg operators, accepted in Computational Methods and Function Theory, arXiv:2203.00243. [arXiv]
  5. A. López-García and R.E. McCleary, Asymptotics of the minimum values of Riesz and logarithmic potentials generated by greedy energy sequences on the unit circle, J. Math. Anal. Appl. 508 (2022) 125866, 36 pp. [arXiv]
  6. A. López-García and V.A. Prokhorov, Characteristic polynomials of random banded Hessenberg matrices and Hermite-Padé approximation, Complex Anal. Oper. Theory 15:113 (2021), 25 pp. [arXiv]
  7. A. López-García and R.E. McCleary, Asymptotics of greedy energy sequences on the unit circle and the sphere, J. Math. Anal. Appl. 504 (2021) 125269, 35 pp. [arXiv]
  8. A. López-García and G. López Lagomasino, Nikishin systems on star-like sets: Ratio asymptotics of the associated multiple orthogonal polynomials, II, J. Approx. Theory 250 (2020), 105320, 28 pp. [arXiv]
  9. A. López-García and V.A. Prokhorov, On random polynomials generated by a symmetric three-term recurrence relation, J. Difference Equations Appl. 25 (2019), 1604-1643. [arXiv]
  10. A. López-García and G. López Lagomasino, Nikishin systems on star-like sets: Ratio asymptotics of the associated multiple orthogonal polynomials, J. Approx. Theory 225 (2018), 1-40. [arXiv]
  11. A. López-García and E. Miña-Díaz, Nikishin systems on star-like sets: algebraic properties and weak asymptotics of the associated multiple orthogonal polynomials, (Russian) Mat. Sb. 209 (2018), 139-177; English transl., Sb. Math. 209 (2018), 1051-1088. [arXiv]
  12. A. López-García and D.A. Wagner, Asymptotics of the energy of sections of greedy energy sequences on the unit circle, and some conjectures for general sequences, Comput. Methods Funct. Theory 15 (2015), 721-750. [arXiv]
  13. A.B.J. Kuijlaars and A. López-García, The normal matrix model with a monomial potential, a vector equilibrium problem, and multiple orthogonal polynomials on a star, Nonlinearity 28 (2015), 347-406. [arXiv]
  14. S. Delvaux and A. López,  High-order three-term recursions, Riemann-Hilbert minors and Nikishin systems on star-like sets, Constr. Approx. 37 (2013), 383-453. [arXiv]
  15. S. Delvaux, A. López and G. López Lagomasino,  A family of Nikishin systems with periodic recurrence coefficients, (Russian) Mat. Sb. 204 (2013), 47-78; English transl., Sb. Math. 204 (2013), 43-74. [arXiv]
  16.  A. López García, Asymptotics of multiple orthogonal polynomials for a system of two measures supported on a starlike set, J. Approx. Theory 163 (2011), 1146-1184. [arXiv] [article]
  17. A. López García and E.B. Saff, Asymptotics of Greedy Energy Points, Math. Comp. 79 (2010), 2287-2316. [arXiv] [article]
  18. A. López García, Greedy energy points with external fields, in “Recent Trends in Orthogonal Polynomials and Approximation Theory” (J. Arvesú, F. Marcellán, and A. Martínez-Finkelshtein, eds.), Contemp. Math. 507, 2010, 189-207. [arXiv]
  19. U. Fidalgo Prieto, A. López García, G. López Lagomasino, and V.N. Sorokin, Mixed type multiple orthogonal polynomials for two Nikishin systems, Constr. Approx. 32 (2010), 255-306. [arXiv]
  20. A. López García and G. López Lagomasino, Relative asymptotic of multiple orthogonal polynomials for Nikishin systems, J. Approx. Theory 158 (2009), 214-241. [arXiv] [article]
  21. A. López García and G. López Lagomasino, Ratio asymptotic of Hermite-Padé orthogonal polynomials for Nikishin systems. II, Adv. Math. 218 (2008), 1081-1106. [arXiv] [article]
  22. M.A. Jiménez Pozo and A. López García, Aplicaciones del Álgebra de Boole métrica a la Teoría de la Medida, La Gaceta de la RSME 9.1 (2006), 59-68.

The following are some pdf files of conference and seminar presentations: