Integral Geometry
Download Integral Geometry full books in PDF, epub, and Kindle. Read online free Integral Geometry ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Author | : R.V. Ambartzumian |
Publisher | : Springer Science & Business Media |
Total Pages | : 135 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9400939213 |
Download Stochastic and Integral Geometry Book in PDF, Epub and Kindle
Author | : Sigurdur Helgason |
Publisher | : Springer Science & Business Media |
Total 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
Author | : Victor Palamodov |
Publisher | : Springer Science & Business Media |
Total 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.
Author | : V. A. Sharafutdinov |
Publisher | : Walter de Gruyter |
Total Pages | : 277 |
Release | : 2012-01-02 |
Genre | : Mathematics |
ISBN | : 3110900092 |
Download Integral Geometry of Tensor Fields Book in PDF, Epub and Kindle
The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
Author | : Richard J. Gardner |
Publisher | : Cambridge University Press |
Total Pages | : 7 |
Release | : 2006-06-19 |
Genre | : Mathematics |
ISBN | : 0521866804 |
Download Geometric Tomography Book in PDF, Epub and Kindle
Geometric tomography deals with the retrieval of information about a geometric object from data concerning its projections (shadows) on planes or cross-sections by planes. It is a geometric relative of computerized tomography, which reconstructs an image from X-rays of a human patient. It overlaps with convex geometry, and employs many tools from that area including integral geometry. It also has connections to geometric probing in robotics and to stereology. The main text contains a rigorous treatment of the subject starting from basic concepts and moving up to the research frontier: seventy-two unsolved problems are stated. Each chapter ends with extensive notes, historical remarks, and some biographies. This comprehensive work will be invaluable to specialists in geometry and tomography; the opening chapters can also be read by advanced undergraduate students.
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 | : Steven G. Krantz |
Publisher | : Springer Science & Business Media |
Total Pages | : 344 |
Release | : 2008-12-15 |
Genre | : Mathematics |
ISBN | : 0817646795 |
Download Geometric Integration Theory Book in PDF, Epub and Kindle
This textbook introduces geometric measure theory through the notion of currents. Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Motivating key ideas with examples and figures, this book is a comprehensive introduction ideal for both self-study and for use in the classroom. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for both graduate students and researchers.
Author | : Rolf Schneider |
Publisher | : Springer Science & Business Media |
Total Pages | : 692 |
Release | : 2008-09-08 |
Genre | : Mathematics |
ISBN | : 354078859X |
Download Stochastic and Integral Geometry Book in PDF, Epub and Kindle
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.
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 | : Valery V. Volchkov |
Publisher | : Springer Science & Business Media |
Total Pages | : 596 |
Release | : 2013-01-30 |
Genre | : Mathematics |
ISBN | : 3034805721 |
Download Offbeat Integral Geometry on Symmetric Spaces Book in PDF, Epub and Kindle
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.