Geometric Analysis And Integral Geometry
DOWNLOAD
Download Geometric Analysis And Integral Geometry PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Geometric Analysis And Integral Geometry book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Groups And Geometric Analysis
DOWNLOAD
Author : Sigurdur Helgason
language : en
Publisher: American Mathematical Society
Release Date : 2022-03-17
Groups And Geometric Analysis written by Sigurdur Helgason and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-17 with Mathematics categories.
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.
Integral Geometry And Convolution Equations
DOWNLOAD
Author : V.V. Volchkov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Integral Geometry And Convolution Equations written by V.V. Volchkov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Geometric Aspects Of Harmonic Analysis
DOWNLOAD
Author : Paolo Ciatti
language : en
Publisher: Springer Nature
Release Date : 2021-09-27
Geometric Aspects Of Harmonic Analysis written by Paolo Ciatti and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-27 with Mathematics categories.
This volume originated in talks given in Cortona at the conference "Geometric aspects of harmonic analysis" held in honor of the 70th birthday of Fulvio Ricci. It presents timely syntheses of several major fields of mathematics as well as original research articles contributed by some of the finest mathematicians working in these areas. The subjects dealt with are topics of current interest in closely interrelated areas of Fourier analysis, singular integral operators, oscillatory integral operators, partial differential equations, multilinear harmonic analysis, and several complex variables. The work is addressed to researchers in the field.
Reconstructive Integral Geometry
DOWNLOAD
Author : Victor Palamodov
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Reconstructive Integral Geometry written by Victor Palamodov and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
One hundred years ago (1904) Hermann Minkowski [58] posed a problem: to re 2 construct an even function I on the sphere 8 from knowledge of the integrals MI (C) = fc Ids over big circles C. Paul Funk found an explicit reconstruction formula for I from data of big circle integrals. Johann Radon studied a similar problem for the Eu clidean plane and space. The interest in reconstruction problems like Minkowski Funk's and Radon's has grown tremendously in the last four decades, stimulated by the spectrum of new modalities of image reconstruction. These are X-ray, MRI, gamma and positron radiography, ultrasound, seismic tomography, electron mi croscopy, synthetic radar imaging and others. The physical principles of these methods are very different, however their mathematical models and solution meth ods have very much in common. The umbrella name reconstructive integral geom etryl is used to specify the variety of these problems and methods. The objective of this book is to present in a uniform way the scope of well known and recent results and methods in the reconstructive integral geometry. We do not touch here the problems arising in adaptation of analytic methods to numerical reconstruction algorithms. We refer to the books [61], [62] which are focused on these problems. Various aspects of interplay of integral geometry and differential equations are discussed in Chapters 7 and 8. The results presented here are partially new.
Integral Geometry And Radon Transforms
DOWNLOAD
Author : Sigurdur Helgason
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-17
Integral Geometry And Radon Transforms written by Sigurdur Helgason and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-17 with Mathematics categories.
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
Geometric Analysis
DOWNLOAD
Author : Eric Grinberg
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Geometric Analysis written by Eric Grinberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
This volume contains the refereed proceedings of the Special Session on Geometric Analysis held at the AMS meeting in Philadelphia in October 1991. The term ``geometric analysis'' is being used with increasing frequency in the mathematical community, but its meaning is not entirely fixed. The papers in this collection should help to better define the notion of geometric analysis by illustrating emerging trends in the subject. The topics covered range over a broad spectrum: integral geometry, Radon transforms, geometric inequalities, microlocal analysis, harmonic analysis, analysis on Lie groups and symmetric spaces, and more. Containing articles varying from the expository to the technical, this book presents the latest results in a broad range of analytic and geometric topics.
Stochastic And Integral Geometry
DOWNLOAD
Author : Rolf Schneider
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-08
Stochastic And Integral Geometry written by Rolf Schneider and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-08 with Mathematics categories.
Stochastic geometry deals with models for random geometric structures. Its early beginnings are found in playful geometric probability questions, and it has vigorously developed during recent decades, when an increasing number of real-world applications in various sciences required solid mathematical foundations. Integral geometry studies geometric mean values with respect to invariant measures and is, therefore, the appropriate tool for the investigation of random geometric structures that exhibit invariance under translations or motions. Stochastic and Integral Geometry provides the mathematically oriented reader with a rigorous and detailed introduction to the basic stationary models used in stochastic geometry – random sets, point processes, random mosaics – and to the integral geometry that is needed for their investigation. The interplay between both disciplines is demonstrated by various fundamental results. A chapter on selected problems about geometric probabilities and an outlook to non-stationary models are included, and much additional information is given in the section notes.
Harmonic Analysis And Integral Geometry
DOWNLOAD
Author : Massimo Picardello
language : en
Publisher: CRC Press
Release Date : 2019-05-08
Harmonic Analysis And Integral Geometry written by Massimo Picardello and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-08 with Mathematics categories.
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
Geometric Analysis On Symmetric Spaces
DOWNLOAD
Author : Sigurdur Helgason
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Geometric Analysis On Symmetric Spaces written by Sigurdur Helgason and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
Among Riemannian manifolds, symmetric spaces (in the sense of Cartan) provide an abundant supply of elegant examples, the structures of which are enhanced by the rich theory of semisimple Lie groups. On these spaces, global analysis, particularly integration theory and partial differential operators, arises in a natural way by the requirement of geometric invariance. In Euclidean space these two subjects are related by the Fourier transform. The Peter-Weyl theory for compact groups, and Cartan's refinement of it, provides a way to develop harmonic analysis on compact symmetric spaces. The noncompact symmetric spaces, however, present a multitude of new and natural problems. This book is devoted to geometric analysis on noncompact Riemannian spaces. The exposition in this book is accessible to readers with modest background in semisimple Lie group theory. In particular, familiarity with representation theory is not needed.
Geometric Integration Theory
DOWNLOAD
Author : Hassler Whitney
language : en
Publisher: Courier Corporation
Release Date : 2005-12-10
Geometric Integration Theory written by Hassler Whitney and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-10 with Mathematics categories.
This treatment of geometric integration theory consists of an introduction to classical theory, a postulational approach to general theory, and a section on Lebesgue theory. Covers the theory of the Riemann integral; abstract integration theory; some relations between chains and functions; Lipschitz mappings; chains and additive set functions, more. 1957 edition.