Integral Geometry Radon Transforms And Complex Analysis

Author : Carlos A. Berenstein,Peter F. Ebenfelt,Simon Gindikin,Sigurdur Helgason,Alexander Tumanov
Publisher : Springer
Page : 166 pages
File Size : 43,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540697022

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Integral Geometry, Radon Transforms and Complex Analysis by Carlos A. Berenstein,Peter F. Ebenfelt,Simon Gindikin,Sigurdur Helgason,Alexander Tumanov Pdf

This book contains the notes of five short courses delivered at the "Centro Internazionale Matematico Estivo" session "Integral Geometry, Radon Transforms and Complex Analysis" held in Venice (Italy) in June 1996: three of them deal with various aspects of integral geometry, with a common emphasis on several kinds of Radon transforms, their properties and applications, the other two share a stress on CR manifolds and related problems. All lectures are accessible to a wide audience, and provide self-contained introductions and short surveys on the subjects, as well as detailed expositions of selected results.

Author : Anonim
Publisher : Unknown
Page : 160 pages
File Size : 50,5 Mb
Release : 1998
Category : Electronic
ISBN : OCLC:1136522326

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Integral Geometry, Radon Transforms, and Complex Analysis by Anonim Pdf

Author : Convex Geometry Special Session on Radon Transforms
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 51,7 Mb
Release : 2008
Category : Harmonic analysis
ISBN : 9780821843277

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Radon Transforms, Geometry, and Wavelets by Convex Geometry Special Session on Radon Transforms Pdf

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

Author : V.V. Volchkov
Publisher : Springer Science & Business Media
Page : 454 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401000239

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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 : Eric Todd Quinto,Fulton Gonzalez,Jens Gerlach Christensen
Publisher : American Mathematical Soc.
Page : 299 pages
File Size : 44,7 Mb
Release : 2013
Category : Mathematics
ISBN : 9780821887387

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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 : Leon Ehrenpreis
Publisher : OUP Oxford
Page : 740 pages
File Size : 45,9 Mb
Release : 2003-10-02
Category : Mathematics
ISBN : 9780191523267

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The Universality of the Radon Transform by Leon Ehrenpreis Pdf

Written by a leading scholar in mathematics, this monograph discusses the Radon transform, a field that has wide ranging applications to X-ray technology, partial differential equations, nuclear magnetic resonance scanning, and tomography. In this book, Ehrenpreis focuses on recent research and highlights the strong relationship between high-level pure mathematics and applications of the Radon transform to areas such as medical imaging. The first part of the book discusses parametric and nonparametric Radon transforms, Harmonic Functions and Radon transform on Algebraic Varieties, nonlinear Radon and Fourier transforms, Radon transform on groups, and Radon transform as the interrelation of geometry and analysis. The later parts discuss the extension of solutions of differential equations, Periods of Eisenstein and Poincaré, and some problems of integral geometry arising in tomography. Examples and proofs are provided throughout the book to aid the reader's understanding. This is the latest title in the Oxford Mathematical Monographs, which includes texts and monographs covering many topics of current research interest in pure and applied mathematics. Other titles include: Carbone and Semmes: A graphic apology for symmetry and implicitness; Higson and Roe: Analytic K-Homology; Iwaniec and Martin: Geometric Function Theory and Nonlinear Analysis; Lyons and Qian: System Control and Rough Paths. Also new in paperback Johnson and Lapidus: The Feynman Integral and Feynman's Operational Calculus; Donaldson and Kronheimer: The geometry of four-manifolds.

Author : I. M. Gel'fand,M. I. Graev,N. Ya. Vilenkin
Publisher : Academic Press
Page : 468 pages
File Size : 51,7 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483262253

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Integral Geometry and Representation Theory by I. M. Gel'fand,M. I. Graev,N. Ya. Vilenkin Pdf

Generalized Functions, Volume 5: Integral Geometry and Representation Theory is devoted to the theory of representations, focusing on the group of two-dimensional complex matrices of determinant one. This book emphasizes that the theory of representations is a good example of the use of algebraic and geometric methods in functional analysis, in which transformations are performed not on the points of a space, but on the functions defined on it. The topics discussed include Radon transform on a real affine space, integral transforms in the complex domain, and representations of the group of complex unimodular matrices in two dimensions. The properties of the Fourier transform on G, integral geometry in a space of constant curvature, harmonic analysis on spaces homogeneous with respect to the Lorentz Group, and invariance under translation and dilation are also described. This volume is suitable for mathematicians, specialists, and students learning integral geometry and representation theory.

Author : Robert Deville,J Esterle,V Petkov,A Sebbar,A Yger
Publisher : CRC Press
Page : 288 pages
File Size : 44,9 Mb
Release : 1996-04-30
Category : Mathematics
ISBN : 0582286980

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Complex Analysis, Harmonic Analysis and Applications by Robert Deville,J Esterle,V Petkov,A Sebbar,A Yger Pdf

Multivariable complex analysis and harmonic analysis provide efficient techniques to study many applied mathematical problems. The main objective of a conference held in Bordeaux in June 1995, in honour of Professor Roger Gay, was to connect these mathematical fields with some of their applications. This was also the guideline for the fourteen contributions collected in this volume. Besides presenting new results, each speaker made a substantial effort in order to present an up to date survey of his field of research. All the subjects presented here are very active domains of research: integral geometry (with its relation to X-ray tomography), classical harmonic analysis and orthogonal polynomials, pluricomplex potential theory (with its deep connection with polynomial approximation), complex analytic methods in the theory of partial differentiable operators with constant coefficients (in the spirit of those initiated by Leon Ehrenpreis), Calderon-Zygmund operators and nonlinear operators, oscillatory integrals and resonance, and finally multivariable residue theory in its most recent developments. It is hoped that the reader will find enough insight in the different survey papers presented here to become involved with one of these subjects or to pursue further applications.

Author : Sigurdur Helgason
Publisher : Springer Science & Business Media
Page : 309 pages
File Size : 49,7 Mb
Release : 2010-11-17
Category : Mathematics
ISBN : 9781441960542

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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 : Massimo Picardello
Publisher : CRC Press
Page : 180 pages
File Size : 50,8 Mb
Release : 2019-05-08
Category : Mathematics
ISBN : 9781482285697

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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 : Andrew Markoe
Publisher : Cambridge University Press
Page : 358 pages
File Size : 45,8 Mb
Release : 2006-01-23
Category : Mathematics
ISBN : 9780521793476

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Analytic Tomography by Andrew Markoe Pdf

This study contains elementary introductions to properties of the Radon transform plus coverage of more advanced topics.

Author : Eric Todd Quinto
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 54,5 Mb
Release : 2001
Category : Radon transforms
ISBN : 9780821821350

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Radon Transforms and Tomography by Eric Todd Quinto Pdf

One of the most exciting features of the fields of Radon transforms and tomography is the strong relationship between high-level pure mathematics and applications to areas such as medical imaging and industrial nondestructive evaluation. The proceedings featured in this volume bring together fundamental research articles in the major areas of Radon transforms and tomography. This volume includes expository papers that are of special interest to beginners as well as advanced researchers. Topics include local tomography and wavelets, Lambda tomography and related methods, tomographic methods in RADAR, ultrasound, Radon transforms and differential equations, and the Pompeiu problem. The major themes in Radon transforms and tomography are represented among the research articles. Pure mathematical themes include vector tomography, microlocal analysis, twistor theory, Lie theory, wavelets, harmonic analysis, and distribution theory. The applied articles employ high-quality pure mathematics to solve important practical problems. Effective scanning geometries are developed and tested for a NASA wind tunnel. Algorithms for limited electromagnetic tomographic data and for impedance imaging are developed and tested. Range theorems are proposed to diagnose problems with tomography scanners. Principles are given for the design of X-ray tomography reconstruction algorithms, and numerical examples are provided. This volume offers readers a comprehensive source of fundamental research useful to both beginners and advanced researchers in the fields.

Author : Valery V. Volchkov,Vitaly V. Volchkov
Publisher : Springer Science & Business Media
Page : 596 pages
File Size : 54,6 Mb
Release : 2013-01-30
Category : Mathematics
ISBN : 9783034805728

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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 : Valeriy Volchkov
Publisher : Unknown
Page : 468 pages
File Size : 47,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401000247

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Integral Geometry and Convolution Equations by Valeriy Volchkov Pdf

Author : G.M. Khenkin
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642580116

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Several Complex Variables V by G.M. Khenkin Pdf

This volume of the Encyclopaedia contains three contributions in the field of complex analysis; on mean periodicity and convolutionequations, Yang-Mills fields and the Radon-Penrose transform, and stringtheory. It is immensely useful to graduate students and researchers in complex analysis, differential geometry, quantum field theory, string theory and general relativity.