Group of Weakly Continuous Operators Associated to a Schrödinger type homogeneous model

• DOI: 10.22533/at.ed.4822314045

• Palavras-chave: -

• Keywords: Groups theory, weakly continuous operators, existence of so- lution, Schr¨odinger type equation, distributional problem, periodic distribu- tional space.

• Abstract:

  In this work, we prove the existence and uniqueness of the solution of the Schr¨odinger type homogeneous model 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 group of operators 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.