On positive Hilbert-Schmidt operators
type: Item
instance of: scholarly article
title: On positive Hilbert-Schmidt operators
zbMATH Open document ID: 1288.47046
published in: Integral Equations and Operator Theory
publication date: 2013-04-15T00:00:00Z
review text: The aim of this paper is to provide sufficient conditions on a class of integral self-adjoint Hilbert-Schmidt operators to be positive definite. Namely, given a compact subset \(G\subset \mathbb R^N\) and \(F(x,y)\) a continuous function on \(G\times G\) satisfying \(F(x,y)=\overline{F(y,x)}\), the author considers integral operators of the form \[ Tf(x)=\int_G\exp(F(x,y))f(y)\, dy \] for \(f\in L^2(G,dx)\). Several conditions on \(F\) are provided to guarantee positivity of \(T\) (in the positive definite sense). The research of these questions is motivated by problems in the area of integrable \(N\)-particle systems of elliptic Calogero-Moser type.
reviewed by: P. Tradacete
Mathematics Subject Classification ID: 47G10
zbMATH DE Number: 6153946
zbMATH Keywords: integral operator
zbMATH Keywords: positive-definite operator
author: Simon Ruijsenaars
MaRDI profile type: Publication
full work available at URL: s00020-013-2034-8
OpenAlex ID: W1990175201
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DOI: 10.1007/S00020-013-2034-8
description: scientific article; zbMATH DE number 6153946