SEMIGRUPO DE CONTRACCIÓN EN EL ESPACIO L2([−π, π])

• DOI: 10.22533/at.ed.3173372325104

• Palavras-chave: Space: L2([ π, π]), Hellinger-Toeplitz theorem, Parseval identity, contraction semigroup, existence of solution, norm of the graph.

• Keywords: Space: L2([ π, π]), Hellinger-Toeplitz theorem, Parseval identity, contraction semigroup, existence of solution, norm of the graph.

• Abstract:

  In this work we begin studying the differential operator: Ho in the space: L2([ π, π]). We know that this operator is not bounded, it is densely defined and symmetric and therefore does not admit a symmetric linear extension to the entire space. We introduce a family of operators in the space: L2([ π, π]) and we show that this forms a class contraction semigroup:Co, and it has Ho as its infinitesimal generator. We also prove that if we restrict the domains of that family of operators, they still remain a contraction semigroup.
  Finally, we give results of the existence of a solution to the associated abstract Cauchy problem and properties of continuous dependence of the solution in connection with other norms.