6 papers
Asymptotics of Polynomials Orthogonal on a Cross with a Jacobi-type Weight
Ahmad Barhoumi, Maxim L. Yattselev
We investigate asymptotic behavior of polynomials satisfying non-Hermitian orthogonality relations $$ \int_Δs^kQ_n(s)ρ(s)\dd s =0, \quad k\in\{0,\ldots,n-1\}, $$ where $…
An asymptotic expansion for the expected number of real zeros of real random polynomials spanned by OPUC
Hanan Aljubran, Maxim L. Yattselev
Let be a sequence of orthonormal polynomials on the unit circle with respect to a positive Borel measure that is symmetric with respect to conjugation…
Self-adjoint Jacobi matrices on trees and multiple orthogonal polynomials
Alexander I. Aptekarev, Sergey A. Denisov, Maxim L. Yattselev
We consider a set of measures on the real line and the corresponding system of multiple orthogonal polynomials (MOPs) of the first and second type. Under some very mild assumptions…
The reciprocal Mahler ensembles of random polynomials
Christopher D. Sinclair, Maxim L. Yattselev
We consider the roots of uniformly chosen complex and real reciprocal polynomials of degree whose Mahler measure is bounded by a constant. After a change of variables this redu…
Ratios of Norms for Polynomials and Connected n-width Problems
V. A. Prokhorov, E. B. Saff, M. Yattselev
Let G be a bounded simply connected domain and E be a regular compact subset of G with connected complement. We investigate the asymptotic behavior of the Kolmogorov k-width, k=k(n…
Multipoint Padé Approximants to Complex Cauchy Transforms with Polar Singularities
L. Baratchart, M. Yattselev
We study diagonal multipoint Padé approximants to sums of a Cauchy transform of a complex measure and a rational function. The measure is assumed to have compact regular support in…