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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Dynamical approach to some problems in integral geometry

Author: Boris Paneah
Translated by:
Journal: Trans. Amer. Math. Soc. 356 (2004), 2757-2780
MSC (2000): Primary 45E99, 39B22; Secondary 37E99, 35L35
Published electronically: December 15, 2003
MathSciNet review: 2052596
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Abstract: As is well known, the main problem in integral geometry is to reconstruct a function in a given domain $D$, where its integrals over a family of subdomains in $D$ are known. Such a problem is interesting not only as an object of pure analysis, but also in connection with various applications in practical disciplines. The most remarkable example of such a connection is the Radon problem and tomography. In this paper we solve one of these problems when $D$ is a bounded domain in ${\mathbb{R}}^2$ with a piecewise smooth boundary. Some intermediate results related to dynamical systems with two generators and to some functional-integral equations are new and interesting per se. As an application of the results obtained we briefly study a boundary problem for a general third order hyperbolic partial differential equation in a bounded domain $D\subset {\mathbb{R}}^2$ with data on the whole boundary $\partial D$.

References [Enhancements On Off] (What's this?)

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Additional Information

Boris Paneah
Affiliation: Department of Mathematics, Technion, Haifa, 32000, Israel

Received by editor(s): February 8, 2002
Received by editor(s) in revised form: January 28, 2003
Published electronically: December 15, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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