This article is cited in 5 papers

Behaviour at infinity of solutions of twisted convolution equations

V. V. Volchkov, Vit. V. Volchkov

Donetsk National University

Abstract: We obtain a precise characterization of the minimal rate of growth at infinity of non-trivial solutions of twisted convolution equations in unbounded domains of $\mathbb{C}^n$. As an application, we obtain definitive versions of the two-radii theorem for twisted spherical means.

Keywords: Heisenberg group, twisted convolution equation, two-radii theorem, confluent hypergeometric functions.

UDC: 517.444

MSC: 43A80, 44A35, 45E10

Received: 12.10.2010

DOI: 10.4213/im5405

 English version: Izvestiya: Mathematics, 2012, 76:1, 79–93

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