Nonlocal time-multipoint problem for a certain class of evolutionary pseudodifferential equations with variable symbols: I

Abstract

It has been proved that in generalized spaces of the type S, a pseudodifferential operator constructed based on a variable symbol can be treated as the operator of infiniteorder differentiation if the operator symbol satisfies certain conditions. The properties of the fundamental solution to a nonlocal time-multipoint problem for the evolutionary equation with this operator have been studied.