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Izvestiya: Mathematics, 2004, Volume 68, Issue 5, Pages 1051–1061
DOI: https://doi.org/10.1070/IM2004v068n05ABEH000508 (Mi im508) 		 
This article is cited in 5 scientific papers (total in 5 papers)

A generalization of the Funk–Hecke theorem to the case of hyperbolic spaces

T. V. Shtepina
English version PDF (172 kB) Citations (5)
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DOI: https://doi.org/10.1070/IM2004v068n05ABEH000508
Abstract: The well-known Funk–Hecke theorem states that for integral operators whose kernels depend only on the distance between points in spherical geometry and where the integral is taken over the surface of a hypersphere, every surface spherical harmonic is an eigenvector. In this paper we extend this theorem to the case of non-compact Lobachevsky spaces. We compute the corresponding eigenvalue in some physically important cases.
Received: 28.11.2003
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2004, Volume 68, Issue 5, Pages 213–224
DOI: https://doi.org/10.4213/im508
Bibliographic databases:
UDC: 515.12
MSC: 42A38, 42B10, 35P05, 47F05, 35J05
Language: English
Original paper language: Russian
Citation: T. V. Shtepina, “A generalization of the Funk–Hecke theorem to the case of hyperbolic spaces”, Izv. RAN. Ser. Mat., 68:5 (2004), 213–224; Izv. Math., 68:5 (2004), 1051–1061
Citation in format AMSBIB
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\pages 213--224
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\transl
\jour Izv. Math.
\yr 2004
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\pages 1051--1061
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  • https://doi.org/10.1070/IM2004v068n05ABEH000508
  • https://www.mathnet.ru/eng/im/v68/i5/p213
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:638
    Russian version PDF:266
    English version PDF:47
    References:70
    First page:1
     
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