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2019 On a special integral equation with an exponential parameter in the kernel
Zhang Honghu
J. Integral Equations Applications 31(3): 431-464 (2019). DOI: 10.1216/JIE-2019-31-3-431

Abstract

Applying Laplace transform on a generalized acoustical radiosity equation results in a special Fredholm integral equation of the second kind with $\lambda =1$ being the integral coefficient. The kernel of the equation contains a varying exponential complex parameter. The values of the parameter that make $\lambda =1$ be an eigenvalue of the kernel are defined in this paper as $L$-eigenvalues of the kernel, and the corresponding eigenfunctions are called $L$-eigenfunctions. The interest of this study is on the properties of the $L$-eigenvalues, $L$-eigenfunctions and the residues of related function at the $L$-eigenvalues. A set of theorems with a series of lemmas as bases are given and proven. They construct an integrated ensemble to reveal the decay structure of the generalized acoustical radiosity system with finite nonzero initial excitation.

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Zhang Honghu. "On a special integral equation with an exponential parameter in the kernel." J. Integral Equations Applications 31 (3) 431 - 464, 2019. https://doi.org/10.1216/JIE-2019-31-3-431

Information

Published: 2019
First available in Project Euclid: 2 November 2019

zbMATH: 07159851
MathSciNet: MR4027255
Digital Object Identifier: 10.1216/JIE-2019-31-3-431

Subjects:
Primary: 45B05
Secondary: 45C05‎

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.31 • No. 3 • 2019
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