By V.V. Volchkov

indispensable geometry offers with the matter of making a choice on services via their integrals over given households of units. those integrals de?ne the corresponding integraltransformandoneofthemainquestionsinintegralgeometryaskswhen this rework is injective. nonetheless, once we paintings with advanced measures or types, operators seem whose kernels are non-trivial yet which describe vital periods of features. many of the questions coming up the following relate, in a single method or one other, to the convolution equations. many of the popular guides during this ?eld contain the works by means of J. Radon, F. John, J. Delsarte, L. Zalcman, C. A. Berenstein, M. L. Agranovsky and up to date monographs by way of L. H¨ ormander and S. Helgason. until eventually lately examine during this quarter was once conducted normally utilizing the means of the Fourier rework and corresponding equipment of advanced research. lately the current writer has labored out an primarily di?erent method according to the outline of varied functionality areas by way of - pansions in distinct services, which has enabled him to set up absolute best ends up in numerous popular problems.

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