Hilbert scales and Sobolev spaces defined by associated Legendre functions

Authors:
Víctor Domínguez;Norbert Heuer;Francisco-Javier Sayas
Affiliations:
Dep. Ingeniería Matemática e Informática, Universidad Pública de Navarra, Campus de Tudela, 31500 Tudela, Spain;Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chile;Department of Mathematical Sciences, University of Delaware, 532 Ewing Hall, Newark DE 19716, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

In this paper we study the Hilbert scales defined by the associated Legendre functions for arbitrary integer values of the parameter. This problem is equivalent to studying the left-definite spectral theory associated to the modified Legendre equation. We give several characterizations of the spaces as weighted Sobolev spaces and prove identities among the spaces corresponding to the lower regularity index.