Reconstructive Integral Geometry
By: by Victor Palamodov
Series: Monographs in Mathematics -- 98; Monographs in mathematics -- 98.
Publisher: Birkhäuser Basel; Imprint: Birkhäuser
Published: 2004
Place of publication: Basel
Language: eng
Format: [electronic resource] /
Number of pages: 164
ISBN-13: 9783034896290; 9783034879415
Subjects: Integral transforms; Mathematics; Fourier analysis
Description: 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 are collected stressing explicit analytic methods. Another focus consists of the relations between algebraic integral geometry and partial differential equations. A concise basic course in harmonic analysis and distribution theory is given in the first chapter. 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. It will be of particular interest to application oriented readers. Further chapters are devoted to the Funk-Radon transform on algebraic varieties of arbitrary dimension. The material appeals to graduates and researchers in pure and applied mathematics who are interested in image reconstruction, inverse problems or functional analysis.
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