Stochastic and Integral Geometry

Stochastic and Integral Geometry PDF Author: R.V. Ambartzumian
Publisher: Springer Science & Business Media
ISBN: 9400939213
Category : Mathematics
Languages : en
Pages : 135

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Book Description

Stochastic and Integral Geometry

Stochastic and Integral Geometry PDF Author: R.V. Ambartzumian
Publisher: Springer Science & Business Media
ISBN: 9400939213
Category : Mathematics
Languages : en
Pages : 135

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Book Description


Integral Geometry and Radon Transforms

Integral Geometry and Radon Transforms PDF Author: Sigurdur Helgason
Publisher: Springer Science & Business Media
ISBN: 1441960546
Category : Mathematics
Languages : en
Pages : 309

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Book Description
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 Tomography

Geometric Tomography PDF Author: Richard J. Gardner
Publisher: Cambridge University Press
ISBN: 0521866804
Category : Mathematics
Languages : en
Pages : 7

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Book Description
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.

Integral Geometry of Tensor Fields

Integral Geometry of Tensor Fields PDF Author: V. A. Sharafutdinov
Publisher: Walter de Gruyter
ISBN: 3110900092
Category : Mathematics
Languages : en
Pages : 277

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Book Description
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.

Geometric Integration Theory

Geometric Integration Theory PDF Author: Hassler Whitney
Publisher: Princeton University Press
ISBN: 1400877571
Category : Mathematics
Languages : en
Pages : 404

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Book Description
A complete theory of integration as it appears in geometric and physical problems must include integration over oriented r-dimensional domains in n-space; both the integrand and the domain may be variable. This is the primary subject matter of the present book, designed to bring out the underlying geometric and analytic ideas and to give clear and complete proofs of the basic theorems. Originally published in 1957. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Random Sets and Integral Geometry

Random Sets and Integral Geometry PDF Author: Georges Matheron
Publisher: John Wiley & Sons
ISBN:
Category : Mathematics
Languages : en
Pages : 294

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Book Description


Integral Geometry and Convolution Equations

Integral Geometry and Convolution Equations PDF Author: V.V. Volchkov
Publisher: Springer Science & Business Media
ISBN: 9401000239
Category : Mathematics
Languages : en
Pages : 466

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Book Description
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 PDF Author: Sigurdur Helgason
Publisher: American Mathematical Society
ISBN: 0821832115
Category : Mathematics
Languages : en
Pages : 667

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Book Description
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.

Stochastic and Integral Geometry

Stochastic and Integral Geometry PDF Author: Rolf Schneider
Publisher: Springer Science & Business Media
ISBN: 354078859X
Category : Mathematics
Languages : en
Pages : 692

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Book Description
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.

Geometric Integration Theory

Geometric Integration Theory PDF Author: Steven G. Krantz
Publisher: Springer Science & Business Media
ISBN: 0817646795
Category : Mathematics
Languages : en
Pages : 344

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Book Description
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.