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Analogs of the Spherical Transform in the Hyperbolic Plane

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Ukrainian Mathematical Journal Aims and scope

We introduce the notion of “s”-convolution in the hyperbolic plane \( {\mathrm{\mathbb{H}}}^2 \) and consider its properties. Analogs of the Helgason spherical transform in the spaces of compactly supported distributions in \( {\mathrm{\mathbb{H}}}^2 \) are investigated. We prove a Paley–Wiener–Schwartz-type theorem for the indicated transforms.

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Authors and Affiliations

  1. Donetsk National University, Donetsk, Ukraine

    V. S. Vasilyanskaya & Vit. V. Volchkov

Authors
  1. V. S. Vasilyanskaya
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  2. Vit. V. Volchkov
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 4, pp. 469–484, April, 2016.

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Vasilyanskaya, V.S., Volchkov, V.V. Analogs of the Spherical Transform in the Hyperbolic Plane. Ukr Math J 68, 526–544 (2016). https://doi.org/10.1007/s11253-016-1239-9

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  • DOI: https://doi.org/10.1007/s11253-016-1239-9

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