Semigroup of Weakly Continuous Operators Associated to a Schrödinger Equation

• DOI: 10.22533/at.ed.4822314046

• Palavras-chave: -

• Keywords: Semigroups theory, weakly continuous operators, existence of solution, Schrödinger equation, distributional problem, periodic distributional space.

• Abstract:

  In this article, we prove the existence and uniqueness of the solution of the Schr¨odinger equation in the periodic distributional space P ^j.  Furthermore, we prove that the solution depends continuously respect to the initial data in P ^j.

  Introducing a family of weakly continuous operators, we prove that this family is a semigroup in P ^j. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained.

  Finally, we give some remarks derived from this study.