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Reconstructive Integral Geometry by Victor Palamodov Pdf
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.
Reconstruction from Integral Data by Victor Palamodov Pdf
Reconstruction of a function from data of integrals is used for problems arising in diagnostics, including x-ray, positron radiography, ultrasound, scattering, sonar, seismic, impedance, wave tomography, crystallography, photo-thermo-acoustics, photoelastics, and strain tomography. Reconstruction from Integral Data presents both long-standing and recent mathematical results from this field in a uniform way. The book focuses on exact analytic formulas for reconstructing a function or a vector field from data of integrals over lines, rays, circles, arcs, parabolas, hyperbolas, planes, hyperplanes, spheres, and paraboloids. It also addresses range characterizations. Coverage is motivated by both applications and pure mathematics. The book first presents known facts on the classical and attenuated Radon transform. It then deals with reconstructions from data of ray (circle) integrals. The author goes on to cover reconstructions in classical and new geometries. The final chapter collects necessary definitions and elementary facts from geometry and analysis that are not always included in textbooks.
Offbeat Integral Geometry on Symmetric Spaces by Valery V. Volchkov,Vitaly V. Volchkov Pdf
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 The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for various classes of functions, far-reaching generalizations of the two-radii problem, the modern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.
Integral Geometry and Tomography by Andrew Markoe,Eric Todd Quinto Pdf
This volume consists of a collection of papers that brings together fundamental research in Radon transforms, integral geometry, and tomography. It grew out of the Special Session at a Sectional Meeting of the American Mathematical Society in 2004. The book contains very recent work of some of the top researchers in the field. The articles in the book deal with the determination of properties of functions on a manifold by integral theoretic methods, or by determining the geometric structure of subsets of a manifold by analytic methods. Of particular concern are ways of reconstructing an unknown function from some of its projections. Radon transforms were developed at the beginning of the twentieth century by researchers who were motivated by problems in differential geometry, mathematical physics, and partial differential equations. Later, medical applications of these transforms produced breakthroughs in imaging technology that resulted in the 1979 Nobel Prize in Physiology and Medicine for the development of computerized tomography. Today the subject boasts substantial cross-disciplinary interactions, both in pure and applied mathematics as well as medicine, engineering, biology, physics, geosciences, and industrial testing. Therefore, this volume should be of interest to a wide spectrum of researchers both in mathematics and in other fields.
Selected Topics in Integral Geometry by Izrailʹ Moiseevich Gelʹfand,Semen Grigorʹevich Gindikin,Mark Iosifovich Graev Pdf
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.
Integral Geometry and Valuations by Semyon Alesker,Joseph H.G. Fu Pdf
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.
Harmonic Analysis and Integral Geometry by Massimo Picardello Pdf
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 Radon Transforms by Sigurdur Helgason Pdf
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, Radon Transforms and Complex Analysis by Carlos A. Berenstein,Peter F. Ebenfelt,Simon Gindikin,Sigurdur Helgason,Alexander Tumanov Pdf
This book contains the notes of five short courses delivered at the "Centro Internazionale Matematico Estivo" session "Integral Geometry, Radon Transforms and Complex Analysis" held in Venice (Italy) in June 1996: three of them deal with various aspects of integral geometry, with a common emphasis on several kinds of Radon transforms, their properties and applications, the other two share a stress on CR manifolds and related problems. All lectures are accessible to a wide audience, and provide self-contained introductions and short surveys on the subjects, as well as detailed expositions of selected results.
Essentials of integral geometry in a homogenous space are presented and the focus is on the basic results and applications. This book provides the readers with new findings, some being published for the first time and serves as an excellent graduate text.
Selected Topics in Integral Geometry by Izrail_ Moiseevich Gel_fand,Semen Grigor_evich Gindikin,Mark Iosifovich Graev Pdf
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. The present 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. Many of the results in the book were obtained by the authors in the course of their career-long work in integral geometry.
Integral Geometry and Representation Theory by Israe͏̈l Mojseevic Gel'fand,Izrailʹ Moiseevich Gelʹfand,Mark Iosifovich Graev,Naum I︠A︡kovlevich Vilenkin Pdf
Integral Geometry and Tomography by Eric Grinberg,Eric Todd Quinto,American Mathematical Society Pdf
This book contains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Integral Geometry and Tomography, held in June 1989 at Humboldt State University in Arcata, California. The papers collected here represent current research in these two interrelated fields. The articles in pure mathematics range over such diverse areas as combinatorics, geometric inequalities, micro-local analysis, group theory, and harmonic analysis. The interplay between Lie group theory, geometry, harmonic analysis, and Radon transforms is well covered. The papers on tomography reflect current research on X-ray computed tomography, as well as radiation dose planning, radar, and partial differential equations. In addition to describing current research, this book provides a useful perspective on the interplay between the fields. For example, abstract theorems about Radon transforms are used to understand applied mathematics, while applied mathematics motivates some of the results in pure mathematics. Though directed at specialists in the field, the book would also be of interest to others who wish to understand current research in these areas and to witness how they relate to other branches of mathematics.
Combinatorial Integral Geometry by R. V. Ambartzumian Pdf
Good,No Highlights,No Markup,all pages are intact, Slight Shelfwear,may have the corners slightly dented, may have slight color changes/slightly damaged spine.
Integral Geometry and Tomography by Eric Grinberg,Eric Todd Quinto Pdf
This book contains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Integral Geometry and Tomography, held in June 1989 at Humboldt State University in Arcata, California. The papers collected here represent current research in these two interrelated fields. The articles in pure mathematics range over such diverse areas as combinatorics, geometric inequalities, micro-local analysis, group theory, and harmonic analysis. The interplay between Lie group theory, geometry, harmonic analysis, and Radon transforms is well covered.The papers on tomography reflect current research on X-ray computed tomography, as well as radiation dose planning, radar, and partial differential equations. In addition to describing current research, this book provides a useful perspective on the interplay between the fields. For example, abstract theorems about Radon transforms are used to understand applied mathematics, while applied mathematics motivates some of the results in pure mathematics. Though directed at specialists in the field, the book would also be of interest to others who wish to understand current research in these areas and to witness how they relate to other branches of mathematics.
