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Wavelet transform on spaces of type \(W\). (English) Zbl 1167.42012

Function spaces of \(W\)-type were introduced by I. M. Gelfand and G.E. Schilov [Generalized functions. Vol. 3. Theory of differential equations. Academic Press. X (1967; Zbl 0355.46017)] and consist of entire analytic functions with special boundedness conditions. In this paper, the authors show that the wavelet integral transform is a linear continuous map between suitably designed function spaces of \(W\)-type.

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
46F12 Integral transforms in distribution spaces

Citations:

Zbl 0355.46017
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References:

[1] S.J.L. van Eijndhoven and M.J. Kerkhof, The Hankel transformation and spaces of type \(W\) , in Reports on applied and numerical analysis , Department of Mathematics and Computing Science, Eindhoven University of Technology, 1988.
[2] I.M. Gelfand and G.E. Shilov, Generalized functions , Vol. III, Academic Press, New York, 1967.
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