Convolution operators on Kucera-type spaces for the Hankel transformation. (English) Zbl 0903.46038

Betancor, J. J.; Marrero, I.

Czech. Math. J. 47, No. 1, 47-72 (1997).

This paper fits into the series of papers of the same authors on the same subject. It is a direct continuation of the paper [Appl. Anal. 52, 103-124 (1994; Zbl 0840.46020)]. The Hankel integral transformation was defined on distribution spaces by A. H. Zemianin. The space \({\mathcal H}_{\mu }\) of all smooth, complex-valued functions satisfying some conditions is endowed with the structure of Fréchet space, there is an automorphism \({\mathbf h}_{\mu }\). On its dual is defined generalized Hankel transformation as a transpose of \({\mathbf h}_{\mu }\). There is a chain of Hilbert spaces \({\mathcal H}^p_{mu}\) included in \({\mathcal H}_{\mu }\), with the property, \(\text{projlim } {\mathcal H}^p_{\mu }\) = \({\mathcal H}_{\mu }\), \(\text{indlim } {\mathcal H}^p_{\mu }\) = \({\mathcal H}_{\mu}'\). Completion of investigation of the multipliers and Hankel convolutions on these space is given.

Reviewer: J.Bureš (Praha)

MSC:

46F12	Integral transforms in distribution spaces
44A15	Special integral transforms (Legendre, Hilbert, etc.)

Keywords:

convolution operators; Hankel integral transformation; generalized Hankel transformation; multipliers; Hankel convolutions

Citations:

Zbl 0840.46020

References:

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