A maximum entropy principle for contractive interpolants
type: Item
instance of: scholarly article
title: A maximum entropy principle for contractive interpolants
zbMATH Open document ID: 0588.47020
DOI: 10.1016/0022-1236(86)90018-2
author: Harry Dym
author: I. Gohberg
published in: Journal of Functional Analysis
publication date: 1986-01-01T00:00:00Z
review text: In this paper a maximum entropy principle is established for a class of continuous contractive \(m\times n\) matrix valued functions g with preassigned Fourier coefficients \(g_ j=\gamma_ j\) for \(j=0,1,... \). The function g in this class which achieves the maximum entropy is characterized in a number of different ways and its entropy is computed in terms of a Hankel operator based on the prescribed matrices \(\gamma_ 0,\gamma_ 1,... \). A pair of seemingly new Szegö type formulas are obtained enroute and some applications to Nevanlinna-Pick interpolation are indicated.
Mathematics Subject Classification ID: 47A56
Mathematics Subject Classification ID: 47A20
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 47B37
zbMATH DE Number: 3944590
zbMATH Keywords: band extensions
zbMATH Keywords: positive extensions
zbMATH Keywords: Szegö formulas
zbMATH Keywords: entropy inequalities
zbMATH Keywords: maximum entropy principle
zbMATH Keywords: Hankel operator
zbMATH Keywords: Szegö type formulas
zbMATH Keywords: Nevanlinna-Pick interpolation
MaRDI profile type: Publication
full work available at URL: 0022-1236(86)90018-2
OpenAlex ID: W2081314711
cites work: Infinite Hankel block matrices and related extension problems
cites work: Hilbert spaces of analytic functions, inverse scattering and operator models. II
cites work: Q3949476
cites work: Problem of search of the minimum of entropy in indeterminate extension problems
cites work: Q3219333
cites work: Q3902017
cites work: The structure of the Naimark dilation and Gaussian stationary processes
cites work: Q4180817
cites work: Factorization of matrix functions and singular integral operators
cites work: Q3894416
cites work: Orthogonal polynomial matrices on the unit circle
cites work: Q3961353
cites work: Extensions of kernels of Fredholm operators
cites work: Unitary interpolants, factorization indices and infinite Hankel Block matrices
cites work: Q3247378
cites work: On invertibility of finite sections of toeplitz matrices
Recommended article: Q3776911
Recommended article: Q3806227
Recommended article: Q3756837
Recommended article: Convexity and regularity properties for entropic interpolations
Recommended article: Entropy and multivariable interpolation
Recommended article: Q5409010
Recommended article: An entropic interpolation proof of the HWI inequality
Recommended article: Q3434795
Recommended article: Q4546139
Recommended article: Interpolation estimates for entropy numbers with applications to non-convex bodies
description: scientific article; zbMATH DE number 3944590