22 citations · 84 across the 10 of their papers we have counts for
11 papers
Tschebyshev-Padé approximations for multivalued functions
Evguenii A. Rakhmanov, Sergey P. Suetin
We discuss the relation between the linear Tschebyshev-Padé approximations to analytic function and the diagonal type I Hermite-Padé polynomials for the tuple of functions $[1,…
Zero distribution for Angelesco Hermite--Padé polynomials
Evguenii A. Rakhmanov
We consider the problem of zero distribution of the first kind Hermite--Padé polynomials associated with a vector function whose components are f…
Do orthogonal polynomials dream of symmetric curves?
A. Martinez-Finkelshtein, E. A. Rakhmanov
The complex or non-hermitian orthogonal polynomials with analytic weights are ubiquitous in several areas such as approximation theory, random matrix models, theoretical physics an…
Gonchar-Stahl's -theorem and associated directions in the theory of rational approximation of analytic functions
E. A. Rakhmanov
Gonchar-Stahl's -theorem characterizes the rate of convergence of best uniform (Chebyshev) rational approximations (with free poles) for one basic class of analytic functions.…
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…
Orthogonal Polynomials and -curves
E. A. Rakhmanov
This paper is devoted to a study of -curves, that is systems of curves in the complex plane whose equilibrium potential in a harmonic external field satisfies a special symmetry…
On the convergence on nonlinear Padé--Chebyshev approximations to the multivalued analytic functions, variation of equilibrium energy and -property of stationary compacts
Andrei A. Gonchar, Evguenii A. Rakhmanov, Sergey P. Suetin
Some new results on the convergence of nonlinear diagonal Padé--Chebyshev approximations to multivalued analytic function given on the segment , are proved. We show that th…
Existence and Regularity for an Energy Maximization Problem in Two Dimensions
Spyridon Kamvissis, Evguenii A. Rakhmanov
We consider the variational problem of maximizing the weighted equilibrium Green's energy of a distribution of charges free to move in a subset of the upper half-plane, under a par…
On asymptotic behavior of Heine-Stieltjes and Van Vleck polynomials
A. Martinez-Finkelshtein, E. A. Rakhmanov
We investigate the strong asymptotics of Heine-Stieltjes polynomials - polynomial solutions of a second order differential equations with complex polynomial coefficients. The solut…
Critical measures, quadratic differentials, and weak limits of zeros of Stieltjes polynomials
A. Martinez-Finkelshtein, E. A. Rakhmanov
We investigate the asymptotic zero distribution of Heine-Stieltjes polynomials - polynomial solutions of a second order differential equations with complex polynomial coefficients.…
Asymptotic upper bounds for the entropy of orthogonal polynomials in the Szegő class
B. Beckermann, A. Martinez-Finkelshtein, E. A. Rakhmanov +1
We give an asymptotic upper bound as for the entropy integral where is the th degree orthonormal polynomial w…