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Integral Geometry and Convolution Equations (Hardcover)
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Integral Geometry and Convolution Equations (Hardcover)
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Integral geometry deals with the problem of determining functions
by their integrals over given families of sets. These integrals
de?ne the corresponding
integraltransformandoneofthemainquestionsinintegralgeometryaskswhen
this transform is injective. On the other hand, when we work with
complex measures or forms, operators appear whose kernels are
non-trivial but which describe important classes of functions. Most
of the questions arising here relate, in one way or another, to the
convolution equations. Some of the well known publications in this
?eld include the works by J. Radon, F. John, J. Delsarte, L.
Zalcman, C. A. Berenstein, M. L. Agranovsky and recent monographs
by L. H] ormander and S. Helgason. Until recently research in this
area was carried out mostly using the technique of the Fourier
transform and corresponding methods of complex analysis. In recent
years the present author has worked out an essentially di?erent
methodology based on the description of various function spaces in
terms of - pansions in special functions, which has enabled him to
establish best possible results in several well known problems."
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