On The Class Of Linear Operators Associated With The Multiparameter Spectral Theory

Abstract

Multiparameter Spectral Theory covers a broad class of problems linked to operator families depending on many spectral parameters given in general forms, as well as operators represented by differential and other types of functional equations. This theory has been stimulated by mathematical physics, particularly by abstracting from the method of separation of variables to solve boundary value problems. The present work is devoted to the study and discussion of a class of operators originated from Multiparameter Spectral Theory, some historical notes on the interpretations and misrepresentations of this class of operators and multiparameter problems in general.