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Izv. RAN. Ser. Mat., 2010, Volume 74, Issue 4, Pages 33–62 (Mi izv2798)  
This article is cited in 1 scientific paper (total in 1 paper)

On a problem of Berenstein–Gay and its generalizations

V. V. Volchkov, Vit. V. Volchkov

Donetsk National University

Abstract: We obtain a solution of the Berenstein–Gay problem on the local analogue of spectral analysis on Riemannian symmetric spaces $X$ of rank 1. The proof is based on constructing transmutation maps connected with eigenfunction expansions of the Laplace–Beltrami operator on $X$.

Keywords: spectral analysis, functions periodic on average, symmetric spaces.

DOI: https://doi.org/10.4213/im2798

Full text: PDF file (708 kB)
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English version:
Izvestiya: Mathematics, 2010, 74:4, 691–721

Bibliographic databases:

UDC: 517.444+517.988.28
MSC: 43A85, 22E30, 43A90, 44A35, 53C35, 53C65
Received: 28.04.2008

Citation: V. V. Volchkov, Vit. V. Volchkov, “On a problem of Berenstein–Gay and its generalizations”, Izv. RAN. Ser. Mat., 74:4 (2010), 33–62; Izv. Math., 74:4 (2010), 691–721

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Volchkov, Vit. V. Volchkov, “Spherical means on two-point homogeneous spaces and applications”, Izv. Math., 77:2 (2013), 223–252  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    		• Èçâåñòèÿ Ðîññèéñêîé àêàäåìèè íàóê. Ñåðèÿ ìàòåìàòè÷åñêàÿ Izvestiya: Mathematics
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