On an existence theory for the double series inverse

摘要

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, Æquations 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) 213–220) 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.