RT info:eu-repo/semantics/article
T1 Groups, Jacobi functions, and rigged Hilbert spaces
A1 Celeghini, Enrico
A1 Gadella Urquiza, Manuel
A1 Olmo Martínez, Mariano Antonio del
AB This paper is a contribution to the study of the relations between special functions, Lie algebrasand rigged Hilbert spaces. The discrete indices and continuous variables of special functions arein correspondence with the representations of their algebra of symmetry, that induce discrete andcontinuous bases coexisting on a rigged Hilbert space supporting the representation. Meaningfuloperators are shown to be continuous on the spaces of test vectors and its dual. Here, the chosenspecial functions, called “Algebraic Jacobi Functions” are related to the Jacobi polynomials andthe Lie algebra is su(2, 2). These functions with m and q fixed, also exhibit a su(1, 1)-symmetry.Different discrete and continuous bases are introduced. An extension in the spirit of the associatedLegendre polynomials and the spherical harmonics is presented introducing the “Jacobi Harmonics”that are a generalization of the spherical harmonics to the three-dimensional hypersphere S3.
SN 0022-2488
YR 2020
FD 2020
LK http://uvadoc.uva.es/handle/10324/40868
UL http://uvadoc.uva.es/handle/10324/40868
LA eng
NO J. Math. Phys. 61 (2020) 033508
DS UVaDOC
RD 22-nov-2024