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Reconstructive Integral Geometry
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Book Synopsis Reconstructive Integral Geometry by : Victor Palamodov
Download or read book Reconstructive Integral Geometry written by Victor Palamodov and published by Birkhäuser. This book was released on 2012-12-06 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Reconstruction from Integral Data by : Victor Palamodov
Download or read book Reconstruction from Integral Data written by Victor Palamodov and published by CRC Press. This book was released on 2016-04-27 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reconstruction of a function from data of integrals is used for problems arising in diagnostics, including x-ray, positron radiography, ultrasound, scattering, sonar, seismic, impedance, wave tomography, crystallography, photo-thermo-acoustics, photoelastics, and strain tomography. Reconstruction from Integral Data presents both long-standing and r
Book Synopsis Offbeat Integral Geometry on Symmetric Spaces by : Valery V. Volchkov
Download or read book Offbeat Integral Geometry on Symmetric Spaces written by Valery V. Volchkov and published by Springer Science & Business Media. This book was released on 2013-01-30 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for various classes of functions, far-reaching generalizations of the two-radii problem, the modern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.
Book Synopsis Complex-Analytic Methods in Reconstructive Integral Geometry by : Nicholas McMurray Hoell
Download or read book Complex-Analytic Methods in Reconstructive Integral Geometry written by Nicholas McMurray Hoell and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This serves as a prelude to a new result for an explicit formula for inverting the attenuated ray transform in such settings modulo a Fredholm error. We close with an appendix on containing all useful geometrical jargon used throughout.
Book Synopsis Integral Geometry and Tomography by : Andrew Markoe
Download or read book Integral Geometry and Tomography written by Andrew Markoe and published by American Mathematical Soc.. This book was released on 2006 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Selected Topics in Integral Geometry by : Izrailʹ Moiseevich Gelʹfand
Download or read book Selected Topics in Integral Geometry written by Izrailʹ Moiseevich Gelʹfand and published by American Mathematical Soc.. This book was released on 2003 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Integral Geometry and Convolution Equations by : V.V. Volchkov
Download or read book Integral Geometry and Convolution Equations written by V.V. Volchkov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Selected Topics in Integral Geometry by : Izrail_ Moiseevich Gel_fand
Download or read book Selected Topics in Integral Geometry written by Izrail_ Moiseevich Gel_fand and published by American Mathematical Soc.. This book was released on 2003-09-02 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. The present 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. Many of the results in the book were obtained by the authors in the course of their career-long work in integral geometry.
Book Synopsis Integral Geometry and Geometric Probability by : Luis A. Santaló
Download or read book Integral Geometry and Geometric Probability written by Luis A. Santaló and published by Cambridge University Press. This book was released on 2004-10-28 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic text on integral geometry now available in paperback in the Cambridge Mathematical Library.
Book Synopsis Topics in Integral Geometry by : De-lin Ren
Download or read book Topics in Integral Geometry written by De-lin Ren and published by World Scientific. This book was released on 1994 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Essentials of integral geometry in a homogenous space are presented and the focus is on the basic results and applications. This book provides the readers with new findings, some being published for the first time and serves as an excellent graduate text.
Book Synopsis Integral Geometry and Convolution Equations by : Valeriy Volchkov
Download or read book Integral Geometry and Convolution Equations written by Valeriy Volchkov and published by . This book was released on 2014-01-15 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Integral Geometry and Tomography by : Eric Grinberg
Download or read book Integral Geometry and Tomography written by Eric Grinberg and published by American Mathematical Soc.. This book was released on 1990 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Integral Geometry and Tomography, held in June 1989 at Humboldt State University in Arcata, California. This book features articles that range over such diverse areas as combinatorics, geometric inequalities, micro-local analysis, group theory, and harmonic analysis.
Book Synopsis Integral Geometry by : Robert L. Bryant
Download or read book Integral Geometry written by Robert L. Bryant and published by . This book was released on 1987 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topic of integral geometry is not as well known as its counterpart, differential geometry. However, research in integral geometry has indicated that this field may yield as equally deep insights as differential geometry has into the global and local nature of manifolds and the functions on them. In 1984, an AMS-IMS-SIAM joint summer research conference on integral geometry was held at Bowdoin College. This volume consists of papers presented there. The papers range from purely expository to quite technical and represent a good survey of contemporary work in integral geometry. Three major areas are covered: the classical problems of computing geometric invariants by statistical averaging procedures; the circle of ideas concerning the Radon transform, going back to the seminal work of Funck and Radon around 1916-1917; and integral-geometric transforms which are now being used in the study of field equations in mathematical physics. Some of these areas also involve group-representation theoretic problems.
Book Synopsis Integral Geometry and Representation Theory by :
Download or read book Integral Geometry and Representation Theory written by and published by . This book was released on 1988 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Radon Transforms, Geometry, and Wavelets by : Gestur Ólafsson
Download or read book Radon Transforms, Geometry, and Wavelets written by Gestur Ólafsson and published by American Mathematical Soc.. This book was released on 2008 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on two special sessions held at the AMS Annual Meeting in New Orleans in January 2007, and a satellite workshop held in Baton Rouge on January 4-5, 2007. It consists of invited expositions that together represent a broad spectrum of fields, stressing surprising interactions and connections between areas that are normally thought of as disparate. The main topics are geometry and integral transforms. On the one side are harmonic analysis, symmetric spaces,representation theory (the groups include continuous and discrete, finite and infinite, compact and non-compact), operator theory, PDE, and mathematical probability. Moving in the applied direction we encounter wavelets, fractals, and engineering topics such as frames and signal and image processing.The subjects covered in this book form a unified whole, and they stand at the crossroads of pure and applied mathematics. The articles cover a broad range in harmonic analysis, with the main themes related to integral geometry, the Radon transform, wavelets and frame theory. These themes can loosely be grouped together as follows:Frame Theory and ApplicationsHarmonic Analysis and Function SpacesHarmonic Analysis and Number TheoryIntegral Geometry and Radon TransformsMultiresolution Analysis, Wavelets, and Applications
Book Synopsis Introduction to Integral Geometry by : Luis A. Santalo
Download or read book Introduction to Integral Geometry written by Luis A. Santalo and published by . This book was released on 1953 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Integral Geometry and Radon Transforms by : Sigurdur Helgason
Download or read book Integral Geometry and Radon Transforms written by Sigurdur Helgason and published by Springer Science & Business Media. This book was released on 2010-11-17 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
