Integral Geometry And Convolution Equations

Author : V.V. Volchkov
Publisher : Springer Science & Business Media
Page : 454 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401000239

Get Book

Integral Geometry and Convolution Equations by V.V. Volchkov Pdf

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.

Author : Valeriy Volchkov
Publisher : Unknown
Page : 468 pages
File Size : 52,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401000247

Get Book

Integral Geometry and Convolution Equations by Valeriy Volchkov Pdf

Author : H. M. Srivastava,R. G. Buschman
Publisher : New York : Wiley
Page : 180 pages
File Size : 43,6 Mb
Release : 1977
Category : Convolutions (Mathematics).
ISBN : UCAL:B4407031

Get Book

Convolution Integral Equations, with Special Function Kernels by H. M. Srivastava,R. G. Buschman Pdf

Author : Hari M. Srivastava,R.G. Buschman
Publisher : Springer Science & Business Media
Page : 259 pages
File Size : 54,7 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9789401580922

Get Book

Theory and Applications of Convolution Integral Equations by Hari M. Srivastava,R.G. Buschman Pdf

This volume presents a state-of-the-art account of the theory and applications of integral equations of convolution type, and of certain classes of integro-differential and non-linear integral equations. An extensive and well-motivated discussion of some open questions and of various important directions for further research is also presented. The book has been written so as to be self-contained, and includes a list of symbols with their definitions. For users of convolution integral equations, the volume contains numerous, well-classified inversion tables which correspond to the various convolutions and intervals of integration. It also has an extensive, up-to-date bibliography. The convolution integral equations which are considered arise naturally from a large variety of physical situations and it is felt that the types of solutions discussed will be usefull in many diverse disciplines of applied mathematics and mathematical physical. For researchers and graduate students in the mathematical and physical sciences whose work involves the solution of integral equations.

Author : Victor Palamodov
Publisher : Birkhäuser
Page : 171 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034879415

Get Book

Reconstructive Integral Geometry by Victor Palamodov Pdf

This book covers facts and methods for the reconstruction of a function in a real affine or projective space from data of integrals, particularly over lines, planes, and spheres. Recent results stress explicit analytic methods. Coverage includes the relations between algebraic integral geometry and partial differential equations. The first half of the book includes the ray, the spherical mean transforms in the plane or in 3-space, and inversion from incomplete data.

Author : Izrailʹ Moiseevich Gelʹfand,Semen Grigorʹevich Gindikin,Mark Iosifovich Graev
Publisher : American Mathematical Soc.
Page : 136 pages
File Size : 40,5 Mb
Release : 2003
Category : Integral geometry
ISBN : 0821829327

Get Book

Selected Topics in Integral Geometry by Izrailʹ Moiseevich Gelʹfand,Semen Grigorʹevich Gindikin,Mark Iosifovich Graev Pdf

The miracle of integral geometry is that it is often possible to recover a function on a manifold just from the knowledge of its integrals over certain submanifolds. The founding example is the Radon transform, introduced at the beginning of the 20th century. Since then, many other transforms were found, and the general theory was developed. Moreover, many important practical applications were discovered. The best known, but by no means the only one, being to medical tomography. This book is a general introduction to integral geometry, the first from this point of view for almost four decades. The authors, all leading experts in the field, represent one of the most influential schools in integral geometry. The book presents in detail basic examples of integral geometry problems, such as the Radon transform on the plane and in space, the John transform, the Minkowski-Funk transform, integral geometry on the hyperbolic plane and in the hyperbolic space, the horospherical transform and its relation to representations of $SL(2,\mathbb C)$, integral geometry on quadrics, etc. The study of these examples allows the authors to explain important general topics of integral geometry, such as the Cavalieri conditions, local and nonlocal inversion formulas, and overdetermined problems in integral geometry. Many of the results in the book were obtained by the authors in the course of their career-long work in integral geometry. This book is suitable for graduate students and researchers working in integral geometry and its applications.

Author : Eric Todd Quinto,Fulton Gonzalez,Jens Gerlach Christensen
Publisher : American Mathematical Soc.
Page : 299 pages
File Size : 40,8 Mb
Release : 2013
Category : Mathematics
ISBN : 9780821887387

Get Book

Geometric Analysis and Integral Geometry by Eric Todd Quinto,Fulton Gonzalez,Jens Gerlach Christensen Pdf

Provides an historical overview of several decades in integral geometry and geometric analysis as well as recent advances in these fields and closely related areas. It contains several articles focusing on the mathematical work of Sigurdur Helgason, including an overview of his research by Gestur Olafsson and Robert Stanton.

Author : Sigurdur Helgason
Publisher : Springer Science & Business Media
Page : 309 pages
File Size : 41,9 Mb
Release : 2010-11-17
Category : Mathematics
ISBN : 9781441960542

Get Book

Integral Geometry and Radon Transforms by Sigurdur Helgason Pdf

In this text, integral geometry deals with Radon’s problem of representing a function on a manifold in terms of its integrals over certain submanifolds—hence the term the Radon transform. Examples and far-reaching generalizations lead to fundamental problems such as: (i) injectivity, (ii) inversion formulas, (iii) support questions, (iv) applications (e.g., to tomography, partial di erential equations and group representations). For the case of the plane, the inversion theorem and the support theorem have had major applications in medicine through tomography and CAT scanning. While containing some recent research, the book is aimed at beginning graduate students for classroom use or self-study. A number of exercises point to further results with documentation. From the reviews: “Integral Geometry is a fascinating area, where numerous branches of mathematics meet together. the contents of the book is concentrated around the duality and double vibration, which is realized through the masterful treatment of a variety of examples. the book is written by an expert, who has made fundamental contributions to the area.” —Boris Rubin, Louisiana State University

Author : Valery V. Volchkov,Vitaly V. Volchkov
Publisher : Springer Science & Business Media
Page : 596 pages
File Size : 40,7 Mb
Release : 2013-01-30
Category : Mathematics
ISBN : 9783034805728

Get Book

Offbeat Integral Geometry on Symmetric Spaces by Valery V. Volchkov,Vitaly V. Volchkov Pdf

The book demonstrates the development of integral geometry on domains of homogeneous spaces since 1990. It covers a wide range of topics, including analysis on multidimensional Euclidean domains and Riemannian symmetric spaces of arbitrary ranks as well as recent work on phase space and the Heisenberg group. The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for various classes of functions, far-reaching generalizations of the two-radii problem, the modern versions of the Pompeiu problem, and explicit reconstruction formulae in problems of integral geometry. These results are intriguing and useful in various fields of contemporary mathematics. The proofs given are “minimal” in the sense that they involve only those concepts and facts which are indispensable for the essence of the subject. Each chapter provides a historical perspective on the results presented and includes many interesting open problems. Readers will find this book relevant to harmonic analysis on homogeneous spaces, invariant spaces theory, integral transforms on symmetric spaces and the Heisenberg group, integral equations, special functions, and transmutation operators theory.

Author : Massimo Picardello
Publisher : CRC Press
Page : 180 pages
File Size : 50,9 Mb
Release : 2019-05-08
Category : Mathematics
ISBN : 9781482285697

Get Book

Harmonic Analysis and Integral Geometry by Massimo Picardello Pdf

Comprising a selection of expository and research papers, Harmonic Analysis and Integral Geometry grew from presentations offered at the July 1998 Summer University of Safi, Morocco-an annual, advanced research school and congress. This lively and very successful event drew the attendance of many top researchers, who offered both individual lecture

Author : L szl¢ Sz‚kelyhidi
Publisher : World Scientific
Page : 180 pages
File Size : 54,5 Mb
Release : 1991
Category : Mathematics
ISBN : 9810206585

Get Book

Convolution Type Functional Equations on Topological Abelian Groups by L szl¢ Sz‚kelyhidi Pdf

This book is devoted to the possible applications of spectral analysis and spectral synthesis for convolution type functional equations on topological abelian groups. The solution space of convolution type equations has been synthesized in the sense that the general solutions are built up from exponential monomial solutions. In particular, equivalence of systems of functional equations can be tested. This leads to a unified treatment of classical equations and to interesting new results.

Author : Leonid Lerer,Vadim Olshevsky,Leiba Rodman
Publisher : Birkhäuser
Page : 240 pages
File Size : 46,8 Mb
Release : 2011-04-08
Category : Mathematics
ISBN : 3764389575

Get Book

Convolution Equations and Singular Integral Operators by Leonid Lerer,Vadim Olshevsky,Leiba Rodman Pdf

This book consists of translations into English of several pioneering papers in the areas of discrete and continuous convolution operators and on the theory of singular integral operators published originally in Russian. The papers were wr- ten more than thirty years ago, but time showed their importance and growing in?uence in pure and applied mathematics and engineering. The book is divided into two parts. The ?rst ?ve papers, written by I. Gohberg and G. Heinig, form the ?rst part. They are related to the inversion of ?nite block Toeplitz matrices and their continuous analogs (direct and inverse problems) and the theory of discrete and continuous resultants. The second part consists of eight papers by I. Gohberg and N. Krupnik. They are devoted to the theory of one dimensional singular integral operators with discontinuous co- cients on various spaces. Special attention is paid to localization theory, structure of the symbol, and equations with shifts. ThisbookgivesanEnglishspeakingreaderauniqueopportunitytogetfam- iarized with groundbreaking work on the theory of Toepliz matrices and singular integral operators which by now have become classical. In the process of the preparation of the book the translator and the editors took care of several misprints and unessential misstatements. The editors would like to thank the translator A. Karlovich for the thorough job he has done. Our work on this book was started when Israel Gohberg was still alive. We see this book as our tribute to a great mathematician.

Author : Shaker A. Meguid
Publisher : Springer
Page : 733 pages
File Size : 54,8 Mb
Release : 2013-12-20
Category : Science
ISBN : 9789400907737

Get Book

Surface Engineering by Shaker A. Meguid Pdf

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.

Author : Andrew Markoe,Eric Todd Quinto
Publisher : American Mathematical Soc.
Page : 180 pages
File Size : 55,9 Mb
Release : 2006
Category : Mathematics
ISBN : 0821857355

Get Book

Integral Geometry and Tomography by Andrew Markoe,Eric Todd Quinto Pdf

This volume consists of a collection of papers that brings together fundamental research in Radon transforms, integral geometry, and tomography. It grew out of the Special Session at a Sectional Meeting of the American Mathematical Society in 2004. The book contains very recent work of some of the top researchers in the field. The articles in the book deal with the determination of properties of functions on a manifold by integral theoretic methods, or by determining the geometricstructure of subsets of a manifold by analytic methods. Of particular concern are ways of reconstructing an unknown function from some of its projections. Radon transforms were developed at the beginning of the twentieth century by researchers who were motivated by problems in differential geometry,mathematical physics, and partial differential equations. Later, medical applications of these transforms produced breakthroughs in imaging technology that resulted in the 1979 Nobel Prize in Physiology and Medicine for the development of computerized tomography. Today the subject boasts substantial cross-disciplinary interactions, both in pure and applied mathematics as well as medicine, engineering, biology, physics, geosciences, and industrial testing. Therefore, this volume should be ofinterest to a wide spectrum of researchers both in mathematics and in other fields.

Author : Israel Gohberg,Izrail Aronovich Fel_dman
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 45,6 Mb
Release : 2005-09-26
Category : Mathematics
ISBN : 0821886657

Get Book

Convolution Equations and Projection Methods for Their Solution by Israel Gohberg,Izrail Aronovich Fel_dman Pdf