Hilbert scales and Sobolev spaces defined by associated Legendre functions

DOI10.1016/j.cam.2010.10.053zbMath1223.46035arXiv0909.4266OpenAlexW2095879986MaRDI QIDQ534231

Norbert Heuer, Víctor Domínguez, Francisco-Javier Sayas

Publication date: 17 May 2011

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.4266

zbMATH Keywords

Hilbert spacesspherical harmonicsLegendre functionsSobolev towers

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Linear symmetric and selfadjoint operators (unbounded) (47B25) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Spherical harmonics (33C55)

Related Items (6)

Sobolev estimates for constructive uniform-grid FFT interpolatory approximations of spherical functions ⋮ Interpolation and cubature approximations and analysis for a class of wideband integrals on the sphere ⋮ Properties and decompositions of domains for powers of the Jacobi differential operator ⋮ Boundary conditions associated with the general left-definite theory for differential operators ⋮ Perspectives on general left-definite theory ⋮ Boundary triples and Weyl \(m\)-functions for powers of the Jacobi differential operator

Cites Work

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• Left-definite theory with applications to orthogonal polynomials
• Inverse acoustic and electromagnetic scattering theory.
• Legendre polynomials, Legendre--Stirling numbers, and the left-definite spectral analysis of the Legendre differential expression
• A short course on operator semigroups
• Acoustic and electromagnetic equations. Integral representations for harmonic problems

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