Open AccessThe $\Theta$-spherical transform and its inversion
Author(s) -
Angela Pasquale
Publication year - 2004
Publication title -
mathematica scandinavica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.553
H-Index - 30
eISSN - 1903-1807
pISSN - 0025-5521
DOI - 10.7146/math.scand.a-14459
Subject(s) - mathematics , laplace transform , inversion (geology) , zonal spherical harmonics , symmetric space , mathematical analysis , pure mathematics , two sided laplace transform , mellin transform , invariant (physics) , spin weighted spherical harmonics , generalization , spherical harmonics , fourier transform , fractional fourier transform , mathematical physics , physics , vector spherical harmonics , paleontology , fourier analysis , structural basin , voltage , quantum mechanics , harmonics , biology
The $\Theta$-spherical transform is defined as a simultaneous generalization of the Harish-Chandra's spherical transform on Riemannian symmetric spaces of noncompact type and of the spherical Laplace transform on noncompactly causal symmetric spaces as defined by Faraut, Hilgert and Ólafsson. An extension of Ólafsson's expansion formula allows us to deduce an inversion formula for the $\Theta$-spherical transform on the space of $W_\Theta$-invariant $C^\infty$ functions with compact support.