V. F. Molchanov, “Spherical functions on hyperboloids”, Math. USSR-Sb., 28:2 (1976), 119

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Mathematics of the USSR-Sbornik, 1976, Volume 28, Issue 2, Pages 119–139
DOI: https://doi.org/10.1070/SM1976v028n02ABEH001643 (Mi sm2743)

This article is cited in 15 scientific papers (total in 15 papers)

Spherical functions on hyperboloids

V. F. Molchanov

English version PDF (1380 kB) Citations (15) Russian version article

References:

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DOI: https://doi.org/10.1070/SM1976v028n02ABEH001643

Abstract: Spherical (zonal) functions on the hyperboloid

- x_{1}^{2} - \dots - x_{p}^{2} + x_{p + 1}^{2} + \dots + x_{p + q}^{2} = 1

$-x_1^2-\dots-x_p^2+x_{p+1}^2+\dots+x_{p+q}^2=1$ corresponding to unitary representations of the group

S O (p, q)

$SO(p,q)$ connected with a cone (RZhMat., 1970, 7B710) are defined and computed.
Bibliography: 15 titles.

Received: 05.03.1974

Bibliographic databases:

UDC: 517.56

MSC: 22E45, 33A75, 43A90

Language: English

Original paper language: Russian

Citation: V. F. Molchanov, “Spherical functions on hyperboloids”, Math. USSR-Sb., 28:2 (1976), 119–139

Citation in format AMSBIB

\Bibitem{Mol76}

\by V.~F.~Molchanov

\paper Spherical functions on hyperboloids

\jour Math. USSR-Sb.

\yr 1976

\vol 28

\issue 2

\pages 119--139

\mathnet{http://mi.mathnet.ru/eng/sm2743}

\crossref{https://doi.org/10.1070/SM1976v028n02ABEH001643}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=451538}

\zmath{https://zbmath.org/?q=an:0333.33012}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1976EM69100001}

Linking options:

https://www.mathnet.ru/eng/sm2743

https://doi.org/10.1070/SM1976v028n02ABEH001643

https://www.mathnet.ru/eng/sm/v141/i2/p139

This publication is cited in the following 15 articles:

Molchanov V.F. Neretin Yu.A., “A Pair of Commuting Hypergeometric Operators on the Complex Plane and Bispectrality”, J. Spectr. Theory, 11:2 (2021), 509–586
Bershtein O., Sinel'shchikov S., “Function Theory on a Q-Analog of Complex Hyperbolic Space”, J. Geom. Phys., 62:5 (2012), 1323–1337
Olga Bershtein, Yevgen Kolisnyk, “Harmonic Analysis on Quantum Complex Hyperbolic Spaces”, SIGMA, 7 (2011), 078, 19 pp.
Artemov A.A., “The Berezin Form and Harmonic Analysis on a Pair of Hyperboloids”, Doklady Mathematics, 84:1 (2011), 437–440
Kowalski K., Rembielinski J., Szczesniak A., “Pseudospherical Functions on a Hyperboloid of One Sheet”, J. Phys. A-Math. Theor., 44:8 (2011), 085302
V. F. Molchanov, “Canonical Representations and Overgroups for Hyperboloids”, Funct. Anal. Appl., 39:4 (2005), 284–295
Ochiai H., “Invariant Distributions on a Non-Isotropic Pseudo-Riemannian Symmetric Space of Rank One”, Indag. Math.-New Ser., 16:3-4 (2005), 631–638
A. A. Artemov, “Poisson transformation for one-sheeted hyperboloids”, Sb. Math., 195:5 (2004), 643–667
Molchanov, VF, “Berezin forms on line bundles over complex hyperbolic spaces”, Integral Equations and Operator Theory, 45:2 (2003), 177
van Dijk G., Sharshov YA., “The Plancherel Formula for Line Bundles on Complex Hyperbolic Spaces”, J. Math. Pures Appl., 79:5 (2000), 451–473
V. F. Molchanov, “Separation of Series for Hyperboloids”, Funct. Anal. Appl., 31:3 (1997), 176–182
Molchanov V., “Holomorphic Discrete Series for Hyperboloids of Hermitian Type”, J. Funct. Anal., 147:1 (1997), 26–50
Smirnov Y., Shustov A., “The Dynamical Group of a Relativistic Oscillator and the Properties of Spherical-Functions on Hyperboloids”, 34, no. 3, 1981, 349–355
Vilenkin N., Klesova L., “The Continuum Parts of the Bases on the Hyperboloid [X,X]=-1”, 31, no. 1, 1980, 108–115
V. F. Molchanov, “Reduction of representations of the complementary series of the $2+3$ de Sitter group with respect to the Lorentz group”, Theoret. and Math. Phys., 37:2 (1978), 1017–1022

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	94

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