Harmonic Analysis and Integral Geometry

Harmonic Analysis and Integral Geometry
Title Harmonic Analysis and Integral Geometry PDF eBook
Author Massimo Picardello
Publisher CRC Press
Pages 180
Release 2019-05-08
Genre Mathematics
ISBN 148228569X

Download Harmonic Analysis and Integral Geometry Book in PDF, Epub and Kindle

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

Harmonic Analysis and Integral Geometry

Harmonic Analysis and Integral Geometry
Title Harmonic Analysis and Integral Geometry PDF eBook
Author Massimo Picardello
Publisher CRC Press
Pages 194
Release 2019-04-15
Genre Mathematics
ISBN 0429530315

Download Harmonic Analysis and Integral Geometry Book in PDF, Epub and Kindle

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

Integral Geometry and Convolution Equations

Integral Geometry and Convolution Equations
Title Integral Geometry and Convolution Equations PDF eBook
Author V.V. Volchkov
Publisher Springer Science & Business Media
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.

Groups and Geometric Analysis

Groups and Geometric Analysis
Title Groups and Geometric Analysis PDF eBook
Author Sigurdur Helgason
Publisher American Mathematical Society
Pages 667
Release 2022-03-17
Genre Mathematics
ISBN 0821832115

Download Groups and Geometric Analysis Book in PDF, Epub and Kindle

Group-theoretic methods have taken an increasingly prominent role in analysis. Some of this change has been due to the writings of Sigurdur Helgason. This book is an introduction to such methods on spaces with symmetry given by the action of a Lie group. The introductory chapter is a self-contained account of the analysis on surfaces of constant curvature. Later chapters cover general cases of the Radon transform, spherical functions, invariant operators, compact symmetric spaces and other topics. This book, together with its companion volume, Geometric Analysis on Symmetric Spaces (AMS Mathematical Surveys and Monographs series, vol. 39, 1994), has become the standard text for this approach to geometric analysis. Sigurdur Helgason was awarded the Steele Prize for outstanding mathematical exposition for Groups and Geometric Analysis and Differential Geometry, Lie Groups and Symmetric Spaces.

Reconstructive Integral Geometry

Reconstructive Integral Geometry
Title Reconstructive Integral Geometry PDF eBook
Author Victor Palamodov
Publisher Springer Science & Business Media
Pages 184
Release 2004-08-20
Genre Mathematics
ISBN 9783764371296

Download Reconstructive Integral Geometry Book in PDF, Epub and Kindle

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.

Integral Geometry and Radon Transforms

Integral Geometry and Radon Transforms
Title Integral Geometry and Radon Transforms PDF eBook
Author Sigurdur Helgason
Publisher Springer Science & Business Media
Pages 309
Release 2010-11-17
Genre Mathematics
ISBN 1441960546

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

Integral Geometry and Valuations

Integral Geometry and Valuations
Title Integral Geometry and Valuations PDF eBook
Author Semyon Alesker
Publisher Springer
Pages 121
Release 2014-10-09
Genre Mathematics
ISBN 3034808747

Download Integral Geometry and Valuations Book in PDF, Epub and Kindle

In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, provides an introduction to the theory of convex valuations with emphasis on recent developments. In particular, it presents the new structures on the space of valuations discovered after Alesker's irreducibility theorem. The newly developed theory of valuations on manifolds is also described. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló. The approach is new and based on the notions and tools presented in the first part. This original viewpoint not only enlightens the classical integral geometry of euclidean space, but it also allows the computation of kinematic formulas in other geometries, such as hermitian spaces. The book will appeal to graduate students and interested researchers from related fields including convex, stochastic, and differential geometry. ​