From Fourier Analysis And Number Theory To Radon Transforms And Geometry

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From Fourier Analysis and Number Theory to Radon Transforms and Geometry

Author : Hershel M. Farkas
Publisher : Springer Science & Business Media
ISBN 13 : 1461440750
Total Pages : 563 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis From Fourier Analysis and Number Theory to Radon Transforms and Geometry by : Hershel M. Farkas

Download or read book From Fourier Analysis and Number Theory to Radon Transforms and Geometry written by Hershel M. Farkas and published by Springer Science & Business Media. This book was released on 2012-09-18 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: A memorial conference for Leon Ehrenpreis was held at Temple University, November 15-16, 2010. In the spirit of Ehrenpreis’s contribution to mathematics, the papers in this volume, written by prominent mathematicians, represent the wide breadth of subjects that Ehrenpreis traversed in his career, including partial differential equations, combinatorics, number theory, complex analysis and a bit of applied mathematics. With the exception of one survey article, the papers in this volume are all new results in the various fields in which Ehrenpreis worked . There are papers in pure analysis, papers in number theory, papers in what may be called applied mathematics such as population biology and parallel refractors and papers in partial differential equations. The mature mathematician will find new mathematics and the advanced graduate student will find many new ideas to explore.A biographical sketch of Leon Ehrenpreis by his daughter, a professional journalist, enhances the memorial tribute and gives the reader a glimpse into the life and career of a great mathematician.

Fourier Analysis and Convexity

Author : Luca Brandolini
Publisher : Springer Science & Business Media
ISBN 13 : 0817681728
Total Pages : 268 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Fourier Analysis and Convexity by : Luca Brandolini

Download or read book Fourier Analysis and Convexity written by Luca Brandolini and published by Springer Science & Business Media. This book was released on 2011-04-27 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explores relationship between Fourier Analysis, convex geometry, and related areas; in the past, study of this relationship has led to important mathematical advances Presents new results and applications to diverse fields such as geometry, number theory, and analysis Contributors are leading experts in their respective fields Will be of interest to both pure and applied mathematicians

Radon Transforms, Geometry, and Wavelets

Author : Convex Geometry Special Session on Radon Transforms
Publisher : American Mathematical Soc.
ISBN 13 : 0821843273
Total Pages : 282 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Radon Transforms, Geometry, and Wavelets by : Convex Geometry Special Session on Radon Transforms

Download or read book Radon Transforms, Geometry, and Wavelets written by Convex Geometry Special Session on Radon Transforms 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

Number Theory, Fourier Analysis and Geometric Discrepancy

Author : Giancarlo Travaglini
Publisher : Cambridge University Press
ISBN 13 : 1139992821
Total Pages : 251 pages
Book Rating : 4.1/5 (399 download)

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Book Synopsis Number Theory, Fourier Analysis and Geometric Discrepancy by : Giancarlo Travaglini

Download or read book Number Theory, Fourier Analysis and Geometric Discrepancy written by Giancarlo Travaglini and published by Cambridge University Press. This book was released on 2014-06-12 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of geometric discrepancy, which provides a framework for quantifying the quality of a distribution of a finite set of points, has experienced significant growth in recent decades. This book provides a self-contained course in number theory, Fourier analysis and geometric discrepancy theory, and the relations between them, at the advanced undergraduate or beginning graduate level. It starts as a traditional course in elementary number theory, and introduces the reader to subsequent material on uniform distribution of infinite sequences, and discrepancy of finite sequences. Both modern and classical aspects of the theory are discussed, such as Weyl's criterion, Benford's law, the Koksma–Hlawka inequality, lattice point problems, and irregularities of distribution for convex bodies. Fourier analysis also features prominently, for which the theory is developed in parallel, including topics such as convergence of Fourier series, one-sided trigonometric approximation, the Poisson summation formula, exponential sums, decay of Fourier transforms, and Bessel functions.

Integral Geometry and Radon Transforms

Author : Sigurdur Helgason
Publisher : Springer Science & Business Media
ISBN 13 : 1441960546
Total Pages : 309 pages
Book Rating : 4.4/5 (419 download)

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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

The Radon Transform

Author : Sigurdur Helgason
Publisher : Springer Science & Business Media
ISBN 13 : 1475714637
Total Pages : 193 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis The Radon Transform by : Sigurdur Helgason

Download or read book The Radon Transform written by Sigurdur Helgason and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this book has been out of print for some time and I have decided to follow the publisher's kind suggestion to prepare a new edition. Many examples with explicit inversion formulas and range theo rems have been added, and the group-theoretic viewpoint emphasized. For example, the integral geometric viewpoint of the Poisson integral for the disk leads to interesting analogies with the X-ray transform in Euclidean 3-space. To preserve the introductory flavor of the book the short and self-contained Chapter Von Schwartz' distributions has been added. Here §5 provides proofs of the needed results about the Riesz potentials while §§3-4 develop the tools from Fourier analysis following closely the account in Hormander's books (1963] and [1983]. There is some overlap with my books (1984] and [1994b] which however rely heavily on Lie group theory. The present book is much more elementary. I am indebted to Sine Jensen for a critical reading of parts of the manuscript and to Hilgert and Schlichtkrull for concrete contributions men tioned at specific places in the text. Finally I thank Jan Wetzel and Bonnie Friedman for their patient and skillful preparation of the manuscript.

Fourier Analysis on Polytopes and the Geometry of Numbers

Author : Sinai Robins
Publisher : American Mathematical Society
ISBN 13 : 1470470330
Total Pages : 352 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Fourier Analysis on Polytopes and the Geometry of Numbers by : Sinai Robins

Download or read book Fourier Analysis on Polytopes and the Geometry of Numbers written by Sinai Robins and published by American Mathematical Society. This book was released on 2024-04-24 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a gentle introduction to the geometry of numbers from a modern Fourier-analytic point of view. One of the main themes is the transfer of geometric knowledge of a polytope to analytic knowledge of its Fourier transform. The Fourier transform preserves all of the information of a polytope, and turns its geometry into analysis. The approach is unique, and streamlines this emerging field by presenting new simple proofs of some basic results of the field. In addition, each chapter is fitted with many exercises, some of which have solutions and hints in an appendix. Thus, an individual learner will have an easier time absorbing the material on their own, or as part of a class. Overall, this book provides an introduction appropriate for an advanced undergraduate, a beginning graduate student, or researcher interested in exploring this important expanding field.

Analysis, Geometry, Number Theory

Author : Leon Ehrenpreis
Publisher : American Mathematical Soc.
ISBN 13 : 0821811487
Total Pages : 508 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Analysis, Geometry, Number Theory by : Leon Ehrenpreis

Download or read book Analysis, Geometry, Number Theory written by Leon Ehrenpreis and published by American Mathematical Soc.. This book was released on 2000 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings from a conference at Temple University celebrating the work of Leon Ehrenpreis, distinguished by its insistence upon getting to the heart of the mathematics and by its astonishing consistency in doing so successfully. Professor Ehrenpreis has worked in many areas of mathematics and has found connections among all of them. For example, we can find his analysis ideas in the context of number theory, geometric thinking within analysis, transcendental number theory tied to partial differential equations.The conference brought together the communities of mathematicians working in the areas of interest to Professor Ehrenpreis and allowed them to share the research inspired by his work. The collection of articles presents current research on PDE's, several complex variables, analytic number theory, integral geometry and tomography. The thinking of Professor Ehrenpreis has contributed fundamental concepts and techniques in these areas and has motivated a wealth of research results. This volume offers a survey of the fundamental principles that unified the conference and influenced the mathematics of Leon Ehrenpreis.

The Universality of the Radon Transform

Author : Leon Ehrenpreis
Publisher : OUP Oxford
ISBN 13 : 0191523267
Total Pages : 740 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis The Universality of the Radon Transform by : Leon Ehrenpreis

Download or read book The Universality of the Radon Transform written by Leon Ehrenpreis and published by OUP Oxford. This book was released on 2003-10-02 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Integral Geometry, Radon Transforms and Complex Analysis

Author : Carlos A. Berenstein
Publisher : Springer
ISBN 13 : 3540697020
Total Pages : 166 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Integral Geometry, Radon Transforms and Complex Analysis by : Carlos A. Berenstein

Download or read book Integral Geometry, Radon Transforms and Complex Analysis written by Carlos A. Berenstein and published by Springer. This book was released on 2006-11-14 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Groups & Geometric Analysis

Author :
Publisher : Academic Press
ISBN 13 : 9780080874326
Total Pages : 654 pages
Book Rating : 4.8/5 (743 download)

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Book Synopsis Groups & Geometric Analysis by :

Download or read book Groups & Geometric Analysis written by and published by Academic Press. This book was released on 1984-06-30 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt: Groups & Geometric Analysis

Groups and Geometric Analysis

Author : Sigurdur Helgason
Publisher : American Mathematical Soc.
ISBN 13 : 0821826735
Total Pages : 693 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Groups and Geometric Analysis by : Sigurdur Helgason

Download or read book Groups and Geometric Analysis written by Sigurdur Helgason and published by American Mathematical Soc.. This book was released on 2000 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, the second of Helgason's impressive three books on Lie groups and the geometry and analysis of symmetric spaces, is an introduction to group-theoretic methods in analysis on spaces with a group action. The first chapter deals with the three two-dimensional spaces of constant curvature, requiring only elementary methods and no Lie theory. It is remarkably accessible and would be suitable for a first-year graduate course. The remainder of the book covers more advanced topics, including the work of Harish-Chandra and others, but especially that of Helgason himself. Indeed, the exposition can be seen as an account of the author's tremendous contributions to the subject.Chapter I deals with modern integral geometry and Radon transforms. The second chapter examines the interconnection between Lie groups and differential operators. Chapter IV develops the theory of spherical functions on semisimple Lie groups with a certain degree of completeness, including a study of Harish-Chandra's $c$-function. The treatment of analysis on compact symmetric spaces (Chapter V) includes some finite-dimensional representation theory for compact Lie groups and Fourier analysis on compact groups. Each chapter ends with exercises (with solutions given at the end of the book!) and historical notes.This book, which is new to the AMS publishing program, is an excellent example of the author's well-known clear and careful writing style. It has become the standard text for the study of spherical functions and invariant differential operators on symmetric spaces. Sigurdur Helgason was awarded the Steele Prize for Groups and Geometric Analysis and the companion volume, ""Differential Geometry, Lie Groups and Symmetric Spaces.""

The Selected Works of Sigurdur Helgason

Author : Sigurdur Helgason
Publisher : American Mathematical Soc.
ISBN 13 : 0821847538
Total Pages : 765 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Selected Works of Sigurdur Helgason by : Sigurdur Helgason

Download or read book The Selected Works of Sigurdur Helgason written by Sigurdur Helgason and published by American Mathematical Soc.. This book was released on 2009 with total page 765 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collects the articles that cover invariant differential operators, geometric properties of solutions to differential equations on symmetric spaces, double fibrations in integral geometry, spherical functions and spherical transforms, duality for symmetric spaces, representation theory, and the Fourier transform on G/K.

Radon Transforms and Tomography

Author : Eric Todd Quinto
Publisher : American Mathematical Soc.
ISBN 13 : 0821821350
Total Pages : 274 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Radon Transforms and Tomography by : Eric Todd Quinto

Download or read book Radon Transforms and Tomography written by Eric Todd Quinto and published by American Mathematical Soc.. This book was released on 2001 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Radon Transform and Medical Imaging

Author : Peter Kuchment
Publisher : SIAM
ISBN 13 : 1611973295
Total Pages : 256 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis The Radon Transform and Medical Imaging by : Peter Kuchment

Download or read book The Radon Transform and Medical Imaging written by Peter Kuchment and published by SIAM. This book was released on 2014-01-01 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys the main mathematical ideas and techniques behind some well-established imaging modalities such as X-ray CT and emission tomography, as well as a variety of newly developing coupled-physics or hybrid techniques, including thermoacoustic tomography. The Radon Transform and Medical Imaging emphasizes mathematical techniques and ideas arising across the spectrum of medical imaging modalities and explains important concepts concerning inversion, stability, incomplete data effects, the role of interior information, and other issues critical to all medical imaging methods. For nonexperts, the author provides appendices that cover background information on notation, Fourier analysis, geometric rays, and linear operators. The vast bibliography, with over 825 entries, directs readers to a wide array of additional information sources on medical imaging for further study.

The Radon Transform, Inverse Problems, and Tomography

Author : Gestur Ólafsson
Publisher : American Mathematical Soc.
ISBN 13 : 0821839306
Total Pages : 176 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Radon Transform, Inverse Problems, and Tomography by : Gestur Ólafsson

Download or read book The Radon Transform, Inverse Problems, and Tomography written by Gestur Ólafsson 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: Since their emergence in 1917, tomography and inverse problems remain active and important fields that combine pure and applied mathematics and provide strong interplay between diverse mathematical problems and applications. The applied side is best known for medical and scientific use, in particular, medical imaging, radiotherapy, and industrial non-destructive testing. Doctors use tomography to see the internal structure of the body or to find functional information, such asmetabolic processes, noninvasively. Scientists discover defects in objects, the topography of the ocean floor, and geological information using X-rays, geophysical measurements, sonar, or other data. This volume, based on the lectures in the Short Course The Radon Transform and Applications to InverseProblems at the American Mathematical Society meeting in Atlanta, GA, January 3-4, 2005, brings together articles on mathematical aspects of tomography and related inverse problems. The articles cover introductory material, theoretical problems, and practical issues in 3-D tomography, impedance imaging, local tomography, wavelet methods, regularization and approximate inverse, sampling, and emission tomography. All contributions are written for a general audience, and the authors have includedreferences for further reading.

Harmonic Analysis and Integral Geometry

Author : Massimo Picardello
Publisher : CRC Press
ISBN 13 : 148228569X
Total Pages : 180 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Harmonic Analysis and Integral Geometry by : Massimo Picardello

Download or read book Harmonic Analysis and Integral Geometry written by Massimo Picardello and published by CRC Press. This book was released on 2019-05-08 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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