Heat and Poisson semigroups for Fourier-Neumann expansions

Given α > -1, consider the second order differential operator in (0, ∞) Lα ≡ (x2d2/dx 2 + (2α + 3)xd/dx + x2 + (α + 1) 2)(f), which appears in the theory of Bessel functions. The purpose of this paper is to develop the corresponding harmonic analysis taking L α as the analogue to the classical La...

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Detalles Bibliográficos
Autores: Betancor, J.J., Ciaurri, O. [0000-0002-1695-3311], Martinez, T., Perez, M. [0000-0002-3050-3712], Torrea, J.L. [0000-0002-3119-6865], Varona, J.L. [0000-0002-2023-9946]
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2006
País:España
Institución:Universidad de La Rioja (UR)
Repositorio:RIUR. Repositorio Institucional de la Universidad de La Rioja
OAI Identifier:oai:portal.dialnet.es:doc/5bbc69c7b750603269e8214c
Acceso en línea:https://investigacion.unirioja.es/documentos/5bbc69c7b750603269e8214c
Access Level:acceso abierto
Palabra clave:Fourier-Neumann expansions
Fractional integrals
Heat semigroup
Poisson semigroup
Riesz potentials
Descripción
Sumario:Given α > -1, consider the second order differential operator in (0, ∞) Lα ≡ (x2d2/dx 2 + (2α + 3)xd/dx + x2 + (α + 1) 2)(f), which appears in the theory of Bessel functions. The purpose of this paper is to develop the corresponding harmonic analysis taking L α as the analogue to the classical Laplacian. Namely we study the boundedness properties of the heat and Poisson semigroups. These boundedness properties allow us to obtain some convergence results that can be used to solve the Cauchy problem for the corresponding heat and Poisson equations. © Springer 2006.