10.—An Abstract Relation for Multiparameter Eigenvalue Problems
Anders Källström, Brian D. Sleeman · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1976
Synopsis Consider the multiparameter system where ut is an element of a separable Hilbert space Hi, i = 1, …, n. The operators Sij are assumed to be bounded symmetric operators in Hi and Ai is assumed self-adjoint. In addition consider the operator equation where B is densely defined and closed in a separable Hilbert space H and Tj, j = 1, …, n is a bounded operator in H. The problem treated in this paper is to seek an expression for a solution v of (**) in terms of the eigenfunctions of the system (*).