International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2004 / Article

Open Access

Volume 2004 |Article ID 194526 | https://doi.org/10.1155/S0161171204301365

Semyon B. Yakubovich, "On the Lebedev transformation in Hardy's spaces", International Journal of Mathematics and Mathematical Sciences, vol. 2004, Article ID 194526, 14 pages, 2004. https://doi.org/10.1155/S0161171204301365

On the Lebedev transformation in Hardy's spaces

Received31 Jan 2003

Abstract

We establish the inverse Lebedev expansion with respect to parameters and arguments of the modified Bessel functions for an arbitrary function from Hardy's space H2,A, A>0. This gives another version of the Fourier-integral-type theorem for the Lebedev transform. The result is generalized for a weighted Hardy space H2,AH2((A,A);|Γ(1+Rez+iτ)|2dτ), 0<A<1, of analytic functions f(z),z=Rez+iτ, in the strip |Rez|A. Boundedness and inversion properties of the Lebedev transformation from this space into the space L2(+;x1dx) are considered. When Rez=0, we derive the familiar Plancherel theorem for the Kontorovich-Lebedev transform.

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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