Analogs of the spherical transform on the hyperbolic plane

• Datum: 2016
• Hauptverfasser: Vasilyanskaya, V. S., Volchkov, V. V., Василянская, В. С., Волчков, Вит. В.
• Format: Artikel
• Sprache: Russisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2016
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/1853
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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.