English

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}
}

Comments

30 pages

R2 v1 2026-06-21T13:49:39.944Z