Hilbert scales and Sobolev spaces defined by associated Legendre functions
Classical Analysis and ODEs
2009-09-24 v1 Numerical Analysis
Spectral Theory
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 study 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 lower regularity index.
Keywords
Cite
@article{arxiv.0909.4266,
title = {Hilbert scales and Sobolev spaces defined by associated Legendre functions},
author = {Victor Dominguez and Norbert Heuer and Francisco-Javier Sayas},
journal= {arXiv preprint arXiv:0909.4266},
year = {2009}
}
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30 pages