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On the Fourier Transform of Causal Distributions
Author(s) -
Trione Susana Elena
Publication year - 1976
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1976554315
Subject(s) - mathematics , fourier transform , operator (biology) , iterated function , distribution (mathematics) , fourier inversion theorem , pure mathematics , combinatorics , mathematical analysis , fourier analysis , fractional fourier transform , chemistry , biochemistry , repressor , transcription factor , gene
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 G α ( P ± i 0, m , n ) [Eq. (I.4.1)] and H α ( P ± i 0,n) [Eq. (II.1.1)]. It follows from Theorem II.3 that H zk ( P ± i 0,n) is, for 2 K ≠ n +2 r , r =0,1..., an elementary solution of the n ‐dimensional ultrahyperbolic operator iterated k times.