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On the Fourier Transform of Causal Distributions

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We extend the distributional Bochner formula [1, p. 72, Theorem 26] to certain kinds of distributions. Theorem I.1 gives a formula [Eq. (I.1.14)] which makes it possible to obtain easily the Fourier transform of distributions of the form As applications of the formula (I.1.14) we evaluate the Fourier transforms of the distributions Gα (P±i0, m, n) [Eq. (I.4.1)] and Hα (P±i0,n) [Eq. (II.1.1)]. It follows from Theorem II.3 that Hzk (P±i0,n) is, for 2Kn+2r, r=0,1..., an elementary solution of the n‐dimensional ultrahyperbolic operator iterated k times.
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Document Type: Research Article

Affiliations: University of Buenos Aires

Publication date: December 1, 1976

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