Semigroups of class Co on l2(Z)
- Autores: Yolanda S. Santiago Ayala
- Localización: Selecciones Matemáticas, ISSN-e 2411-1783, Vol. 10, Nº. 2, 2023, págs. 273-284
- Idioma: inglés
- DOI: 10.17268/sel.mat.2023.02.04
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Resumen
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.
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