This article is cited 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.

UDC: 517.444+517.988.28

MSC: 43A85, 22E30, 43A90, 44A35, 53C35, 53C65

Received: 28.04.2008

DOI: 10.4213/im2798

 English version: Izvestiya: Mathematics, 2010, 74:4, 691–721

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