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dc.contributor.authorKalnins, Ernie G.
dc.contributor.authorMiller, W., Jr.
dc.date.accessioned2008-10-30T01:43:25Z
dc.date.available2008-10-30T01:43:25Z
dc.date.issued1994-04
dc.identifier.citationKalnins, E.G. & Miller, W., Jr. (1994). Models of q-algebra representations: q-integral transforms and "addition theorems''. Journal of Mathematical Physics, 35, 1951.en_US
dc.identifier.issn0022-2488
dc.identifier.urihttps://hdl.handle.net/10289/1204
dc.description.abstractIn his classic book on group representations and special functions Vilenkin studied the matrix elements of irreducible representations of the Euclidean and oscillator Lie algebras with respect to countable bases of eigenfunctions of the Cartan subalgebras, and he computed the summation identities for Bessel functions and Laguerre polynomials associated with the addition theorems for these matrix elements. He also studied matrix elements of the pseudo-Euclidean and pseudo-oscillator algebras with respect to the continuum bases of generalized eigenfunctions of the Cartan subalgebras of these Lie algebras and this resulted in realizations of the addition theorems for the matrix elements as integral transform identities for Bessel functions and for confluent hypergeometric functions. Here we work out q analogs of these results in which the usual exponential function mapping from the Lie algebra to the Lie group is replaced by the q-exponential mappings Eq and eq. This study of representations of the Euclidean quantum algebra and the q-oscillator algebra (not a quantum algebra) leads to summation, integral transform, and q-integral transform identities for q analogs of the Bessel and confluent hypergeometric functions, extending the results of Vilenkin for the q=1 case.en_US
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.relation.urihttp://link.aip.org/link/?JMAPAQ/35/1951/1en_US
dc.rightsCopyright 1994 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in the Journal of Mathematical Physics and may be found at http://jmp.aip.org/jmp/top.jspen_US
dc.subjectMathematicsen_US
dc.subjectalgebrasen_US
dc.subjectirreducible representationsen_US
dc.subjectlie groupsen_US
dc.subjectmatrix elementsen_US
dc.subjectintegral transformationsen_US
dc.subjecthypergeometric functionsen_US
dc.subjectbessel functionsen_US
dc.subjectsymmetry groupsen_US
dc.subjectmellin transformen_US
dc.subjectoscillatorsen_US
dc.subjecteigenfunctionsen_US
dc.subjectquantum mechanicsen_US
dc.titleModels of q-algebra representations: q-integral transforms and "addition theorems''en_US
dc.typeJournal Articleen_US
dc.identifier.doi10.1063/1.530581en_US
dc.relation.isPartOfJournal of Mathematical Physicsen_NZ
pubs.begin-page1951en_NZ
pubs.elements-id84095
pubs.end-page1975en_NZ
pubs.issue4en_NZ
pubs.volume35en_NZ


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