6 citations · 7 across the 7 of their papers we have counts for
7 papers
Weighted equilibrium in a field of a uniform charge of an interval
James Kessinger, Andrei Martinez-Finkelshtein
We study the logarithmic equilibrium problem on the interval in the presence of an external field generated by a uniform background charge supported on the same interval.…
Elliptic orthogonal polynomials and OPRL
Victor Alves, Andrei Martinez-Finkelshtein
We explore a class of meromorphic functions on elliptic curves, termed \emph{elliptic orthogonal a-polynomials} (-EOPs), which extend the classical notion of orthogonal polynomi…
Zeros of orthogonal little q-Jacobi polynomials: interlacing and monotonicity
Andrei Martinez-Finkelshtein, Rafael Morales, Daniel Perales
We investigate the distribution of zeros of the little q-Jacobi polynomials and related q-hypergeometric families. We prove that the zeros of these orthogonal polynomials exhibit s…
Sampling patterns for Zernike-like bases in non-standard geometries
Sergio Díaz-Elbal, Andrei Martínez-Finkelshtein, Darío Ramos-López
Zernike polynomials are widely used in optics and ophthalmology due to their direct connection to classical optical aberrations. While orthogonal on the unit disk, their applicatio…
Zeros of generalized hypergeometric polynomials via finite free convolution. Applications to multiple orthogonality
Andrei Martinez-Finkelshtein, Rafael Morales, Daniel Perales
We address the problem of the weak asymptotic behavior of zeros of families of generalized hypergeometric polynomials as their degree tends to infinity. The main tool is the repres…
Electrostatic partners and zeros of orthogonal and multiple orthogonal polynomials
Andrei Martínez-Finkelshtein, Ramón Orive, Joaquín Sánchez-Lara
For a given polynomial with simple zeros, and a given semiclassical weight , we present a construction that yields a linear second-order differential equation (ODE), and in…
Phase transitions and equilibrium measures in random matrix models
A. Martinez-Finkelshtein, R. Orive, E. A. Rakhmanov
The paper is devoted to a study of phase transitions in the Hermitian random matrix models with a polynomial potential. In an alternative equivalent language, we study families of…