On the Fourier Transform of Causal Distributions |
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Authors: | Susana Elena Trione |
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Abstract: | 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 2K≠n+2r, r=0,1..., an elementary solution of the n-dimensional ultrahyperbolic operator iterated k times. |
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