On the Fourier transforms of retarded Lorentz-invariant functions

En:

J. Math. Anal. Appl. 1981;84(1):73-112

Fecha:

1981

Formato:

application/pdf

Tipo de documento:

info:eu-repo/semantics/article
info:ar-repo/semantics/artículo
info:eu-repo/semantics/publishedVersion

Descriptores:

MATHEMATICAL TRANSFORMATIONS

Descripción:

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.

Identificador(es):

http://hdl.handle.net/20.500.12110/paper_0022247X_v84_n1_p73_Trione

Derechos:

info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar