相关论文: Some computable Wiener-Hopf determinants and polyn…
The continuous analogue of a Toeplitz determinant identity for Wiener-Hopf operators is proved. An example which arises from random matrix theory is studied and an error term for the asymptotics of the determinant is computed.
The purpose of this paper is to describe asymptotic formulas for determinants of certain operators that are analogues of Wiener-Hopf operators. The determinant formulas yield information about the distribution functions for certain random…
Inspired by the paper of Groenewald, Kaashoek and Ran (Wiener-Hopf indices of unitary functions on the unit circle in terms of realizations and related results on Toeplitz operators. \emph{Indag. Math.} 28, (2017), 649-710), we present an…
We establish an asymptotic formula for determinants of truncated Wiener-Hopf+Hankel operators with symbol equal to the exponential of a constant times the characteristic function of an interval. This is done by reducing it to the…
The solution of a problem arising in integrable systems requires sharp asymptotics for the inverses and determinants of truncated Wiener-Hopf operators, both in the regular case (where the non-truncated Wiener-Hopf operator is invertible)…
In the work we propose an algorithm for a Wiener -- Hopf factorization of scalar polynomials based on notions of indices and essential polynomials. The algorithm uses computations with finite Toeplitz matrices and permits to obtain…
We derive the asymptotic behavior of determinants of truncated Wiener-Hopf operators generated by symbols having Fisher-Hartwig singularities. This task is achieved thanks to an asymptotic resolution of the Riemann-Hilbert problem…
The purpose of this paper is to compute the asymptotics of determinants of finite sections of operators that are trace class perturbations of Toeplitz operators. For example, we consider the asymptotics in the case where the matrices are of…
We study the determinants of Toeplitz matrices as the size of the matrices tends to infinity, in the particular case where the symbol has two jump discontinuities and tends to zero on an arc of the unit circle at a sufficiently fast rate.…
This paper is concerned with the Wiener-Hopf indices of unimodular rational matrix functions on the imaginary axis. These indices play a role in the Fredholm theory for Wiener-Hopf integral operators. Our main result gives formulas for the…
Some preliminaries and basic facts regarding unbounded Wiener-Hopf operators (WH) are provided. WH with rational symbols are studied in detail showing that they are densely defined closed and have finite dimensional kernels and deficiency…
In recent developments, a general approach for solving Riemann--Hilbert problems numerically has been developed. We review this numerical framework, and apply it to the calculation of orthogonal polynomials on the real line. Combining this…
We derive an asymptotic expansion for a Wiener-Hopf determinant arising in the problem of counting one-dimensional free fermions on a line segment at zero temperature. This expansion is an extension of the result in the theory of Toeplitz…
Orthogonal polynomials on the unit circle are completely determined by their reflection coefficients through the Szeg\H{o} recurrences. We assume that the reflection coefficients converge to some complex number a with 0 < |a| < 1. The…
In this paper we show, how a straightforward and natural application of a pair of fundamental identities valid for polynomials orthogonal over the unit circle, can be used to calculate the determinant of the finite Toeplitz matrix, $$…
Wiener-Hopf factorisation plays an important role in the theory of Toeplitz operators. We consider here Toeplitz operators in the Hardy spaces $H^p$ of the upper half-plane and we review how their Fredholm properties can be studied in terms…
In this paper we determine the asymptotics of the determinants of truncated Wiener-Hopf plus Hankel operators $\det(W_R(a)\pm H_R(a))$ as $R$ tends to infinity for symbols $a(x)=(x^2/(1+x^2))^\beta$ with the parameter $\beta$ being of small…
We give an effective method to compute the entropy for polynomials orthogonal on a segment of the real axis that uses as input data only the coefficients of the recurrence relation satisfied by these polynomials. This algorithm is based on…
Let $w$ be a semiclassical weight which is generic in Magnus's sense, and $(p_n)_{n=0}^\infty$ the corresponding sequence of orthogonal polynomials. The paper expresses the Christoffel--Darboux kernel as a sum of products of Hankel integral…
In this paper we are going to prove two asymptotic formulas for determinants det(I-K_s), as s goes to infinity, where K_s are the Wiener-Hopf-Hankel operators acting on L^2[0,s] with the kernels K(x-y)+K(x+y) and K(x-y)-K(x+y),…