Offbeat Integral Geometry On Symmetric Spaces
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Author | : Valery V. Volchkov |
Publisher | : Springer Science & Business Media |
Total Pages | : 596 |
Release | : 2013-01-30 |
Genre | : Mathematics |
ISBN | : 3034805721 |
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 The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for various classes of functions, far-reaching generalizations of the two-radii problem, the modern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.
Author | : Eric Liviu Grinberg |
Publisher | : |
Total Pages | : 202 |
Release | : 1983 |
Genre | : Integral geometry |
ISBN | : |
Author | : Sigurdur Helgason |
Publisher | : American Mathematical Soc. |
Total Pages | : 670 |
Release | : 1993 |
Genre | : Mathematics |
ISBN | : 9780821874875 |
Author | : Phillip Griffiths |
Publisher | : American Mathematical Society(RI) |
Total Pages | : 657 |
Release | : 2008 |
Genre | : Electronic books |
ISBN | : 9781470412661 |
Author | : I. M. Gel'fand |
Publisher | : Academic Press |
Total Pages | : 468 |
Release | : 2014-05-12 |
Genre | : Mathematics |
ISBN | : 1483262251 |
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 | : Boris Rubin |
Publisher | : Cambridge University Press |
Total Pages | : 595 |
Release | : 2015-11-12 |
Genre | : Mathematics |
ISBN | : 0521854598 |
A comprehensive introduction to basic operators of integral geometry and the relevant harmonic analysis for students and researchers.
Author | : Victor Palamodov |
Publisher | : Birkhäuser |
Total Pages | : 171 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034879415 |
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 | : Martha Abell |
Publisher | : Springer Nature |
Total Pages | : 373 |
Release | : 2019-10-21 |
Genre | : Mathematics |
ISBN | : 3030122778 |
Different aspects of harmonic analysis, complex analysis, sampling theory, approximation theory and related topics are covered in this volume. The topics included are Fourier analysis, Padè approximation, dynamical systems and difference operators, splines, Christoffel functions, best approximation, discrepancy theory and Jackson-type theorems of approximation. The articles of this collection were originated from the International Conference in Approximation Theory, held in Savannah, GA in 2017, and organized by the editors of this volume.
Author | : Izrailʹ Moiseevich Gelʹfand |
Publisher | : American Mathematical Soc. |
Total Pages | : 136 |
Release | : 2003 |
Genre | : Integral geometry |
ISBN | : 9780821829325 |
The miracle of integral geometry is that it is often possible to recover a function on a manifold just from the knowledge of its integrals over certain submanifolds. The founding example is the Radon transform, introduced at the beginning of the 20th century. Since then, many other transforms were found, and the general theory was developed. Moreover, many important practical applications were discovered. The best known, but by no means the only one, being to medical tomography. This book is a general introduction to integral geometry, the first from this point of view for almost four decades. The authors, all leading experts in the field, represent one of the most influential schools in integral geometry. The book presents in detail basic examples of integral geometry problems, such as the Radon transform on the plane and in space, the John transform, the Minkowski-Funk transform, integral geometry on the hyperbolic plane and in the hyperbolic space, the horospherical transform and its relation to representations of $SL(2,\mathbb C)$, integral geometry on quadrics, etc. The study of these examples allows the authors to explain important general topics of integral geometry, such as the Cavalieri conditions, local and nonlocal inversion formulas, and overdetermined problems in integral geometry. Many of the results in the book were obtained by the authors in the course of their career-long work in integral geometry. This book is suitable for graduate students and researchers working in integral geometry and its applications.
Author | : Robert L. Bryant |
Publisher | : |
Total Pages | : 364 |
Release | : 1987 |
Genre | : Mathematics |
ISBN | : |
The topic of integral geometry is not as well known as its counterpart, differential geometry. However, research in integral geometry has indicated that this field may yield as equally deep insights as differential geometry has into the global and local nature of manifolds and the functions on them. In 1984, an AMS-IMS-SIAM joint summer research conference on integral geometry was held at Bowdoin College. This volume consists of papers presented there. The papers range from purely expository to quite technical and represent a good survey of contemporary work in integral geometry. Three major areas are covered: the classical problems of computing geometric invariants by statistical averaging procedures; the circle of ideas concerning the Radon transform, going back to the seminal work of Funck and Radon around 1916-1917; and integral-geometric transforms which are now being used in the study of field equations in mathematical physics. Some of these areas also involve group-representation theoretic problems.