Reconstructive Integral Geometry

Victor Palamodov

ISBN 10: 3034896298 / ISBN 13: 9783034896290

Published by Springer, Basel, Birkhäuser Basel, Birkhäuser Okt 2012, 2012

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -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. 164 pp. Englisch.

Seller Inventory # 9783034896290

Bibliographic Details

• Title: Reconstructive Integral Geometry
• Publisher: Springer, Basel, Birkhäuser Basel, Birkhäuser Okt 2012
• Publication Date: 2012
• Language: English
• ISBN 10: 3034896298
• ISBN 13: 9783034896290
• Binding: Taschenbuch
• Condition: Neu

About this title

Synopsis

These lecture notes treat polynomial identity rings from both the combinatorial and structural points of view. The former studies the ideal of polynomial identities satisfied by a ring. The latter studies the properties of rings which satisfy a polynomial identity.

The greater part of recent research in polynomial identity rings is about combinatorial questions, and the combinatorial part of the lecture notes gives an up-to-date account of recent research. On the other hand, the main structural results have been known for some time, and the emphasis there is on a presentation accessible to newcomers to the subject.

The intended audience is graduate students in algebra, and researchers in algebra, combinatorics and invariant theory.

Review

"This book is an excellent overview of the field of integral geometry with emphasis on the functional analytic and differential geometric aspects. The author proves theorems for some of the most important Radon transforms, including transforms on hyperplanes, k-planes, lines, and spheres, and he investigates incomplete (limited) data problems including microlocal analytic issues...This book contains many treasures in integral geometry...and it belongs on the shelf of any analyst or geometer who would like to see how deep functional analysis and differential geometry are used to solve important problems in integral geometry." ―Mathematical Reviews