Form preserving linear integral operators
type: Item
instance of: scholarly article
title: Form preserving linear integral operators
zbMATH Open document ID: 0855.45008
DOI: 10.1016/0898-1221(96)00036-3
author: Sui Sun Cheng
author: Tzon-Tzer Lu
publication date: 1997-02-04T00:00:00Z
review text: The present paper is concerned with integral operators of the following form \[ (Tf)(t)=\int^1_0K(t,s)f(s)ds,\quad t\in[0,1], \] where the kernel function \(K(t,s)\) is continuous on \([0,1] \times [0,1]\) and input functions are continuous on \([0,1]\). The authors are interested in characterizations of the kernel \(K(t,s)\) such that the corresponding operator \(T\) leaves various families of input functions invariant. Here several of these families including symmetric, skew symmetric, balanced, absolutely balanced functions, and functions with nonnegative symmetric sums are considered and characterizations of the kernel functions are given. In the last section several applications of the obtained results are mentioned. In addition, the authors point out that some results can be extended to square integrable kernel functions and integrable input functions.
Mathematics Subject Classification ID: 45P05
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 47G10
zbMATH DE Number: 915118
zbMATH Keywords: form preserving linear integral operators
zbMATH Keywords: invariance of input functions
reviewed by: Shanli Sun
MaRDI profile type: Publication
full work available at URL: 0898-1221(96)00036-3
OpenAlex ID: W2056057641
cites work: Q3876240
cites work: Q4282918
cites work: Q3907862
cites work: An inequality for an integral quadratic form
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 915118