Zobrazeno 1 - 10
of 198
pro vyhledávání: '"Aptekarev, A. I."'
In this work, we establish strong asymptotics of multiple orthogonal polynomials of the second type for Angelesco systems with measures that satisfy Szeg\H{o} conditions. We consider multi-indices that converge to infinity in the non-marginal directi
Externí odkaz:
http://arxiv.org/abs/2404.14391
Publikováno v:
J. Spectr. Theory, 11(4), 1511-1597, 2021
We continue studying the connection between Jacobi matrices defined on a tree and multiple orthogonal polynomials (MOPs) that was discovered previously by the authors. In this paper, we consider Angelesco systems formed by two analytic weights and ob
Externí odkaz:
http://arxiv.org/abs/2004.04113
A limiting property of the nearest-neighbor recurrence coefficients for multiple orthogonal polynomials from a Nevai class is investigated. Namely, assuming that the nearest-neighbor coefficients have a limit along rays of the lattice, we describe it
Externí odkaz:
http://arxiv.org/abs/1908.04540
Akademický článek
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Publikováno v:
Trans. Amer. Math. Soc., 373(2), 875-917, 2020
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, which are satisfied by Angelesco systems, we define self-adjoint Jac
Externí odkaz:
http://arxiv.org/abs/1806.10531
Akademický článek
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Publikováno v:
Math. Sb., 208(3), 4-27 (2017)
Let $\widehat\sigma$ be a Cauchy transform of a possibly complex-valued Borel measure $\sigma$ and $\{p_n\}$ be a system of orthonormal polynomials with respect to a measure $\mu$, $\mathrm{supp}(\mu)\cap\mathrm{supp}(\sigma)=\varnothing$. An $(m,n)$
Externí odkaz:
http://arxiv.org/abs/1605.09672
Publikováno v:
Eur. Phys. J. B (2016) 89: 85
The R\'enyi entropies $R_{p}[\rho]$, $p>0,\neq 1$ of the highly-excited quantum states of the $D$-dimensional isotropic harmonic oscillator are analytically determined by use of the strong asymptotics of the orthogonal polynomials which control the w
Externí odkaz:
http://arxiv.org/abs/1602.05371
Publikováno v:
SIGMA 12 (2016), 054, 30 pages
In this paper we present multidimensional analogues of both the continuous- and discrete-time Toda lattices. The integrable systems that we consider here have two or more space coordinates. To construct the systems, we generalize the orthogonal polyn
Externí odkaz:
http://arxiv.org/abs/1511.08098
Publikováno v:
Comm. Pure Appl. Math. 70 (2017), 444-510
Hermite-Pad\'e approximants of type II are vectors of rational functions with common denominator that interpolate a given vector of power series at infinity with maximal order. We are interested in the situation when the approximated vector is given
Externí odkaz:
http://arxiv.org/abs/1505.03993