On the Lebedev transformation in Hardy's spaces
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 fo...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204301365 |
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| Summary: | 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 H⌢2,A≡H⌢2((−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(ℝ+;x−1dx) are considered. When Rez=0, we derive the familiar Plancherel theorem for the
Kontorovich-Lebedev transform. |
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| ISSN: | 0161-1712 1687-0425 |