Semigroup of Weakly Continuous Operators Associated to a Generalized Schrödinger Equation

Abstract

In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space ′ P . Furthermore, we prove that the solution depends continuously respect to the initial data in ′ P . Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in ′ P . Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study.