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arXiv · 0909.4266

Hilbert scales and Sobolev spaces defined by associated Legendre functions

Victor Dominguez·Norbert Heuer·Francisco-Javier Sayas
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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 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.

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Victor Dominguez, Norbert Heuer, Francisco-Javier Sayas. 2009-09-23. Hilbert scales and Sobolev spaces defined by associated Legendre functions. https://arxiv.org/abs/0909.4266

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