Integral Geometry Radon Transforms And Complex Analysis PDF Download
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| Author | : Carlos A. Berenstein |
| Publisher | : Springer |
| Total Pages | : 166 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540697020 |
Download Integral Geometry, Radon Transforms and Complex Analysis Book in PDF, ePub and Kindle
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 | : Sigurdur Helgason |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 309 |
| Release | : 2010-10-27 |
| Genre | : Mathematics |
| ISBN | : 1441960554 |
Download Integral Geometry and Radon Transforms Book in PDF, ePub and Kindle
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 | : |
| Publisher | : |
| Total Pages | : 160 |
| Release | : 1998 |
| Genre | : |
| ISBN | : |
Download Integral Geometry, Radon Transforms, and Complex Analysis Book in PDF, ePub and Kindle
| Author | : I. M. Gel'fand |
| Publisher | : Academic Press |
| Total Pages | : 468 |
| Release | : 2014-05-12 |
| Genre | : Mathematics |
| ISBN | : 1483262251 |
Download Integral Geometry and Representation Theory Book in PDF, ePub and Kindle
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 | : Gestur Ólafsson |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 282 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0821843273 |
Download Radon Transforms, Geometry, and Wavelets Book in PDF, ePub and Kindle
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 | : Sigurdur Helgason |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 214 |
| Release | : 1999-08-01 |
| Genre | : Mathematics |
| ISBN | : 9780817641092 |
Download The Radon Transform Book in PDF, ePub and Kindle
The Radon transform is an important topic in integral geometry which deals with the problem of expressing a function on a manifold in terms of its integrals over certain submanifolds. Solutions to such problems have a wide range of applications, namely to partial differential equations, group representations, X-ray technology, nuclear magnetic resonance scanning, and tomography. This second edition, significantly expanded and updated, presents new material taking into account some of the progress made in the field since 1980. Aimed at beginning graduate students, this monograph will be useful in the classroom or as a resource for self-study. Readers will find here an accessible introduction to Radon transform theory, an elegant topic in integral geometry.
| Author | : V.V. Volchkov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 466 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401000239 |
Download Integral Geometry and Convolution Equations Book in PDF, ePub and Kindle
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 | : Leon Ehrenpreis |
| Publisher | : OUP Oxford |
| Total Pages | : 740 |
| Release | : 2003-10-02 |
| Genre | : Mathematics |
| ISBN | : 0191523267 |
Download The Universality of the Radon Transform Book in PDF, ePub and Kindle
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 | : Eric Todd Quinto |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 299 |
| Release | : 2013 |
| Genre | : Mathematics |
| ISBN | : 0821887386 |
Download Geometric Analysis and Integral Geometry Book in PDF, ePub and Kindle
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 | : Boris Rubin |
| Publisher | : Cambridge University Press |
| Total Pages | : 595 |
| Release | : 2015-11-12 |
| Genre | : Mathematics |
| ISBN | : 0521854598 |
Download Introduction to Radon Transforms Book in PDF, ePub and Kindle
A comprehensive introduction to basic operators of integral geometry and the relevant harmonic analysis for students and researchers.
