Reconstructive Integral Geometry
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Beschreibung
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.
Covers a gap in the literature which was caused by the fast development in the field over the last 15-20 years Addressed to researchers in both pure and applied mathematics
Autor*in
Victor Palamodov
Themen in »Reconstructive Integral Geometry«
Fourier analyis Fourier transform Funk transformation Image reconstruction Integral transforms curvature distribution functional analysis harmonic analysis integral transform manifold
Stimmen zu »Reconstructive Integral Geometry«
"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
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