Hilbert scales and Sobolev spaces defined by associated Legendre functions

Details Hilbert scales and Sobolev spaces defined by associated Legendre functions Hilbert scales and Sobolev spaces defined by associated Legendre functions

2009-09-23

arxiv.org/abs/0909.4266v1

Mathematics

Classical Analysis and ODEs

30 pages

Scientific paper

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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