We present different stability estimates for the Jacobi inverse eigenvalue problem. First, we give upper bounds expressed in terms of quadrature data and not having weights in denominators. The technique of orthonormal polynomials and integral representation of Hankel determinants is used. Our bounds exhibit only polynomial growth in the problem’s dimension (see [4]). It has been shown that the...

A class ξ of algebras of symmetric n × n matrices, related to Toeplitz-plus-Hankel structures and including the well-known algebra H diagonalized by the Hartley transform, is investigated. The algebras of ξ are then exploited in a general displacement decomposition of an arbitrary n× n matrix A. Any algebra of ξ is a 1-space, i.e., it is spanned by n matrices having as first rows the vectors of...

The Langlands functoriality conjecture, as reformulated in the “beyond endoscopy” program, predicts comparisons between (stable) trace formulas of different groups G1,G2 for every morphism G1L→LG2 their L-groups. This conjecture can be seen a special case more general which replaces reductive by spherical varieties and formula its generalization, relative formula. goal this article continuation...

Two unitary integral transforms with a very-well poised 7F6-function as a kernel are given. For both integral transforms the inverse is the same as the original transform after an involution on the parameters. The 7F6-function involved can be considered as a non-polynomial extension of the Wilson polynomial, and is therefore called a Wilson function. The two integral transforms are called a Wil...

This paper provides a new proof of the index formula for block Toeplitz operators. The idea is to calculate a certain integral formula for the winding number using Fourier series, expressing this in terms of Hankel operators, and producing the expected index.