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| Titel: |
Generalized n-dimensional hilbert transform and applications |
| Auteur: |
Chaudhry, M.A. Pandey, J.N. |
| Verschenen in: |
Applicable analysis |
| Paginering: | Jaargang 20 (1985) nr. 3-4 pagina's 221-235 |
| Jaar: |
1985-10 |
| Inhoud: |
Let [image omitted] be the Schwartz test function space, consisting of infinitely differentiable functions φ defined over Rn such that φk(x) belongs to [image omitted] for each k=0, 1, 2, 3,…. We shall introduce the space [image omitted] of all test functions [image omitted] of the form.[image omitted] where each [image omitted] and k is finite, and the function [image omitted] We shall prove that [image omitted] with the sub- space topology induced on it by the topology of [image omitted] is dense in [image omitted] The Hilbert transform of test functions in [image omitted] is defined by: [image omitted] It is seen that the operator [image omitted] is a linear embedding and satisfies [image omitted] The Hilbert transforn of test functions [image omitted] is then defined by[image omitted] where [image omitted] is a sequence in [image omitted] converging to φ in the sense of the convergence in [image omitted] . It is seen that [image omitted] is a homeomorphism with its inverse given by [image omitted] The Hilbert transforn Hf of [image omitted] is then defined by [image omitted] It is seen that the generalized Hilbert transform defined by the above relation is a linear isomorphism from [image omitted] onto itself and satisfies [image omitted] Applications of our result to solve some singular integral equations are also shown. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 4 van 10 gevonden artikelen
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