Integral Geometry and Convolution Equations

V V Volchkov

ISBN 10: 140201628X / ISBN 13: 9781402016288

Editore: Springer Okt 2003, 2003

Riguardo questo articolo

Neuware - 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.

Codice articolo 9781402016288

Dati bibliografici

• Titolo: Integral Geometry and Convolution Equations
• Editore: Springer Okt 2003
• Data di pubblicazione: 2003
• Lingua: Inglese
• ISBN 10: 140201628X
• ISBN 13: 9781402016288
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 246 L x 169 A x 29 P (millimetri) 246 millimetri di larghezza per 169 millimetri di altezza per 29 millimetri di profondità
• Peso: 857 grammi

Descrizione articolo

Riassunto

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.

Recensione

From the reviews:

"The book under review reflects the modern state of the results and is mainly based on the results of the author. ... is written in a very clear manner and should be useful both for experts in the field and for postgraduate students. The wide list of citations includes more than 250 items." (Nikolai K. Karapetyants, Zentralblatt MATH, Vol. 1043 (18), 2004)

"The book is devoted to the problem of injectivity for convolution operators of geometric nature. ... A survey of works in the area by other authors is presented as well. The monograph contains a collection of interesting and original results ... . The book will be of interest for specialists in analysis, in particular, in harmonic analysis, spectral theory, invariant function spaces and integral equations. It may serve as a source for further research in the area." (Mark Agranovsky, Mathematical Reviews, Issue 2005 e)