On the Fourier transforms of retarded Lorentz-invariant functions

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In this article we evaluate the Fourier transforms of retarded Lorentz-invariant functions (and distributions) as limits of Laplace transforms. Our method works generally for any retarded Lorentz-invariant functions φ(t) (t ε{lunate} Rn) which is, besides, a continuous function of slow growth. We gi...

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Autor principal: Trione, S.E.
Formato: JOUR
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MATHEMATICAL TRANSFORMATIONS
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0022247X_v84_n1_p73_Trione
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_0022247X_v84_n1_p73_Trione2023-10-03T14:29:26Z On the Fourier transforms of retarded Lorentz-invariant functions Trione, S.E. MATHEMATICAL TRANSFORMATIONS In this article we evaluate the Fourier transforms of retarded Lorentz-invariant functions (and distributions) as limits of Laplace transforms. Our method works generally for any retarded Lorentz-invariant functions φ(t) (t ε{lunate} Rn) which is, besides, a continuous function of slow growth. We give, among others, the Fourier transform of GR(t, α, m2, n) and GA(t, α, m2, n), which, in the particular case α = 1, are the characteristic functions of the volume bounded by the forward and the backward sheets of the hyperboloid u = m2 and by putting α = -k are the derivatives of k-order of the retarded and the advanced-delta on the hyperboloid u = m2. We also obtain the Fourier transform of the function W(t, α, m2, n) introduced by M. Riesz (Comm. Sem. Mat. Univ. Lund4 (1939)). We finish by evaluating the Fourier transforms of the distributional functions GR(t, α, m2, n), GA(t, α, m2, n) and W(t, α, m2, n) in their singular points. © 1981. Fil:Trione, S.E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0022247X_v84_n1_p73_Trione
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic MATHEMATICAL TRANSFORMATIONS
spellingShingle MATHEMATICAL TRANSFORMATIONS
Trione, S.E.
On the Fourier transforms of retarded Lorentz-invariant functions
topic_facet MATHEMATICAL TRANSFORMATIONS
description In this article we evaluate the Fourier transforms of retarded Lorentz-invariant functions (and distributions) as limits of Laplace transforms. Our method works generally for any retarded Lorentz-invariant functions φ(t) (t ε{lunate} Rn) which is, besides, a continuous function of slow growth. We give, among others, the Fourier transform of GR(t, α, m2, n) and GA(t, α, m2, n), which, in the particular case α = 1, are the characteristic functions of the volume bounded by the forward and the backward sheets of the hyperboloid u = m2 and by putting α = -k are the derivatives of k-order of the retarded and the advanced-delta on the hyperboloid u = m2. We also obtain the Fourier transform of the function W(t, α, m2, n) introduced by M. Riesz (Comm. Sem. Mat. Univ. Lund4 (1939)). We finish by evaluating the Fourier transforms of the distributional functions GR(t, α, m2, n), GA(t, α, m2, n) and W(t, α, m2, n) in their singular points. © 1981.
format JOUR
author Trione, S.E.
author_facet Trione, S.E.
author_sort Trione, S.E.
title On the Fourier transforms of retarded Lorentz-invariant functions
title_short On the Fourier transforms of retarded Lorentz-invariant functions
title_full On the Fourier transforms of retarded Lorentz-invariant functions
title_fullStr On the Fourier transforms of retarded Lorentz-invariant functions
title_full_unstemmed On the Fourier transforms of retarded Lorentz-invariant functions
title_sort on the fourier transforms of retarded lorentz-invariant functions
url http://hdl.handle.net/20.500.12110/paper_0022247X_v84_n1_p73_Trione
work_keys_str_mv AT trionese onthefouriertransformsofretardedlorentzinvariantfunctions
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