Semigroups of class Co on l2(Z)

• Autor: Santiago Ayala, Yolanda
• Formato: artículo
• Fecha de Publicación: 2023
• Institución: Universidad Nacional de Trujillo
• Repositorio: Revistas - Universidad Nacional de Trujillo
• Lenguaje: español
• OAI Identifier: oai:ojs.revistas.unitru.edu.pe:article/5560
• Enlace del recurso: https://revistas.unitru.edu.pe/index.php/SSMM/article/view/5560
• Nivel de acceso: acceso abierto
• Materia: l2(Z) space; Hellinger-Toeplitz theorem; generalized multipli- cation operator; Semigroup of contraction; graph norm

In this work we begin by studying the generalized multiplication operator M on the l2(Z). We prove that this operator is not bounded, is densely defined and symmetric and therefore does not admit a symmetric linear extension to the entire space. We introduce a family of operators on the l2(Z) space with n even and demonstrate that it forms a contraction semigroup of class Co, having −M 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 existence of solution of the associated abstract Cauchy problem and properties of continuous dependence of the solution in connection to other norms.