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Abstract:

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.

Registro:

Documento: Artículo
Título:On the Fourier transforms of retarded Lorentz-invariant functions
Autor:Trione, S.E.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina
Instituto Argentino, Matemática Consejo Nacional de Investigaciones Científicas y Técnicas, Buenos Aires, Argentina
Palabras clave:MATHEMATICAL TRANSFORMATIONS
Año:1981
Volumen:84
Número:1
Página de inicio:73
Página de fin:112
DOI: http://dx.doi.org/10.1016/0022-247X(81)90153-0
Título revista:Journal of Mathematical Analysis and Applications
Título revista abreviado:J. Math. Anal. Appl.
ISSN:0022247X
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_0022247X_v84_n1_p73_Trione.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v84_n1_p73_Trione

Referencias:

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  • Constantinescu, (1974) Distributionen und ihre Anwendung in der Physik, , Teubner, Stuttgart
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  • Trione, On the Fourier transforms of retarded Lorentz-invariant functions (1980) Trabajos de Matemática (Publicaciones Previas), 26, , Serie 1, 4th ed., IAM-CONICET

Citas:

---------- APA ----------
(1981) . On the Fourier transforms of retarded Lorentz-invariant functions. Journal of Mathematical Analysis and Applications, 84(1), 73-112.
http://dx.doi.org/10.1016/0022-247X(81)90153-0
---------- CHICAGO ----------
Trione, S.E. "On the Fourier transforms of retarded Lorentz-invariant functions" . Journal of Mathematical Analysis and Applications 84, no. 1 (1981) : 73-112.
http://dx.doi.org/10.1016/0022-247X(81)90153-0
---------- MLA ----------
Trione, S.E. "On the Fourier transforms of retarded Lorentz-invariant functions" . Journal of Mathematical Analysis and Applications, vol. 84, no. 1, 1981, pp. 73-112.
http://dx.doi.org/10.1016/0022-247X(81)90153-0
---------- VANCOUVER ----------
Trione, S.E. On the Fourier transforms of retarded Lorentz-invariant functions. J. Math. Anal. Appl. 1981;84(1):73-112.
http://dx.doi.org/10.1016/0022-247X(81)90153-0