Premium
The inversion problem and applications of the generalized radon transform
Author(s) -
Beylkin Gregory
Publication year - 1984
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160370503
Subject(s) - radon transform , mathematics , fredholm integral equation , inversion (geology) , integral transform , radon , mathematical analysis , integral equation , partial differential equation , operator (biology) , exponential function , physics , biochemistry , chemistry , repressor , structural basin , paleontology , quantum mechanics , gene , transcription factor , biology
We prove that under certain conditions the inversion problem for the generalized Radon transform reduces to solving a Fredholm integral equation and we obtain the asymptotic expansion of the symbol of the integral operator in this equation. We consider applications of the generalized Radon transform to partial differential equations with variable coefficients and provide a solution to the inversion problem for the attenuated and exponential Radon transforms.