2017
Том 69
№ 9

All Issues

Analogs of the spherical transform on the hyperbolic plane

Vasilyanskaya V. S., Volchkov V. V.


Abstract

We introduce the notion of “$s$”-convolution on the hyperbolic plane $H^2$ and consider its properties. Analogs of the Helgason spherical transform on the spaces of compactly supported distributions in $H^2$ are studied. We prove a Paley –Wiener – Schwartz-type theorem for these transforms.

Citation Example: Vasilyanskaya V. S., Volchkov V. V. Analogs of the spherical transform on the hyperbolic plane // Ukr. Mat. Zh. - 2016. - 68, № 4. - pp. 469-484.