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: Artículo publishedVersion
Publicado: 1981
Materias:
MATHEMATICAL TRANSFORMATIONS
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0022247X_v84_n1_p73_Trione
https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v84_n1_p73_Trione_oai
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id I28-R145-paper_0022247X_v84_n1_p73_Trione_oai
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spelling I28-R145-paper_0022247X_v84_n1_p73_Trione_oai2024-08-16 Trione, S.E. 1981 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. application/pdf http://hdl.handle.net/20.500.12110/paper_0022247X_v84_n1_p73_Trione info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Math. Anal. Appl. 1981;84(1):73-112 MATHEMATICAL TRANSFORMATIONS On the Fourier transforms of retarded Lorentz-invariant functions info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v84_n1_p73_Trione_oai
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-145
collection Repositorio Digital de la Universidad de Buenos Aires (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 Artículo
Artículo
publishedVersion
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
publishDate 1981
url http://hdl.handle.net/20.500.12110/paper_0022247X_v84_n1_p73_Trione
https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v84_n1_p73_Trione_oai
work_keys_str_mv AT trionese onthefouriertransformsofretardedlorentzinvariantfunctions
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