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The Cauchy problem for evolution equations with the Bessel operator of infinite order. I

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Abstract

We establish necessary and sufficient conditions under which the Bessel operator of infinite order is bounded in certain spaces. We study properties of the Bessel transformations of distributions from these spaces, those of convolutions, convolutors, and multiplicators.

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Authors and Affiliations

  1. Chernovtsy National University, 2 Kotsyubinskii str., Chernovtsy, 58000, Ukraine

    V. V. Gorodetskii & O. V. Martynyuk

Authors
  1. V. V. Gorodetskii
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  2. O. V. Martynyuk
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Correspondence to O. V. Martynyuk.

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Original Russian Text © V.V. Gorodetskii and O.V. Martynyuk, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 6, pp. 3–15.

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Gorodetskii, V.V., Martynyuk, O.V. The Cauchy problem for evolution equations with the Bessel operator of infinite order. I. Russ Math. 54, 1–12 (2010). https://doi.org/10.3103/S1066369X10060010

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  • DOI: https://doi.org/10.3103/S1066369X10060010

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