Spherical harmonics and rigged Hilbert spaces

Spherical harmonics and rigged Hilbert spaces

This paper is devoted to study discrete and continuous bases for spaces supporting representations of SO(3) and SO(3, 2) where the spherical harmonics are involved. We show how discrete and continuous bases coexist on appropriate choices of rigged Hilbert spaces. We prove the continuity of relevant...

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Veröffentlicht in:Journal of mathematical physics 2018-05, Vol.59 (5)
Hauptverfasser: Celeghini, E., Gadella, M., del Olmo, M. A.
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Sprache:eng
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Algebra
Functionals
Hilbert space
Mathematical analysis
Operators (mathematics)
Quantum physics
Spherical harmonics
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creator Celeghini, E.
Gadella, M.
del Olmo, M. A.
description This paper is devoted to study discrete and continuous bases for spaces supporting representations of SO(3) and SO(3, 2) where the spherical harmonics are involved. We show how discrete and continuous bases coexist on appropriate choices of rigged Hilbert spaces. We prove the continuity of relevant operators and the operators in the algebras spanned by them using appropriate topologies on our spaces. Finally, we discuss the properties of the functionals that form the continuous basis.
doi_str_mv 10.1063/1.5026740
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source AIP Journals Complete; Alma/SFX Local Collection
subjects Algebra
Functionals
Hilbert space
Mathematical analysis
Operators (mathematics)
Quantum physics
Spherical harmonics
title Spherical harmonics and rigged Hilbert spaces
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