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Details van artikel 58 van 62 gevonden artikelen
| Titel: |
The hilbert transform of periodic distributions |
| Auteur: |
Pandey, J. N. |
| Verschenen in: |
Integral transforms and special functions |
| Paginering: | Jaargang 5 (1997) nr. 1-2 pagina's 117-142 |
| Jaar: |
1997-05 |
| Inhoud: |
Let f(t) be a periodic function with period 2τ defined on the real line R. A new definition of the Hilbert transform (Hf)(x) of this function is given by [image omitted] provided this limit exists; the integral in (1) is taken in the Cauchy principal-value sense. It is shown that the definition (1) is equivalent to the conventional definition, [image omitted] where the integral in (2) is taken in the Cauchy principal value sense too. We then use our results to extend the Hilbert transform to periodic distributions of period 2τ defined on the real line, i.e. to [image omitted] is the space of infinitely differentiable functions with period 2τ defined on the real line. An inversion formula over the space [image omitted] is proved. Amongst many other related results which are proved, we have proved the existence of a periodic harmonic function u(xy) (periodic in x with period 2τ) whose boundary values at a semicircular boundary are given. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 58 van 62 gevonden artikelen
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