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On an existence theory for the double series inverse

机译:关于双级数逆的存在理论

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The variational double series solution to sampled Fredholm integral equations of the first kind (N.H.S. Haidar, Approximate double series solution to certain Fredholm integral equations of the first kind, J. Math. Anal. Appl. 143 (1989) 264-289; N.H.S. Haidar, A double series variational method for a class of second kind Fredholm integral equations, Equations Math. 48 (1994) 24-34; N.H.S. Haidar, Recursive pseudo-inversion of the Laplace transform on the real line, Appl. Math. Comput. 84 (1997) 213-310) belongs fundamentally in a certain nonlinearly weighted Sobolev space. We report in this note on a measure-theoretic proof of the existence of this solution. (C) 2000 Published by Elsevier Science Inc. All rights reserved. [References: 11]
机译:采样的第一类Fredholm积分方程的变分双级数解(NHS Haidar,某些第一类Fredholm积分方程的近似双级数解,J。Math。Anal。Appl。143(1989)264-289; NHS Haidar ,一类第二类Fredholm积分方程的双级数变分方法,Equations Math。48(1994)24-34; NHS Haidar,实线上Laplace变换的递归伪逆,Appl。Math。Comput。84 (1997)213-310)基本上属于某个非线性加权的Sobolev空间。我们在本说明中报告了该解决方案存在的度量理论证明。 (C)2000由Elsevier Science Inc.出版。保留所有权利。 [参考:11]

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