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The Universality of the Radon Transform$
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Leon Ehrenpreis

Print publication date: 2003

Print ISBN-13: 9780198509783

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198509783.001.0001

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HARMONIC FUNCTIONS IN R n

HARMONIC FUNCTIONS IN R n

Chapter:
(p.161) 3 HARMONIC FUNCTIONS IN R n
Source:
The Universality of the Radon Transform
Author(s):

Leon Ehrenpreis

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198509783.003.0003

This chapter looks at a variation of “harmonic function” which was introduced by Chevalley. Ordinary harmonic functions are solutions of the Laplace equation; Chevalley harmonic functions are solutions of certain systems of partial differential equations. The equations and the harmonic functions combine to give a tensor product decomposition of the space of functions. This theory is indispensable for extending the concept of Radon transform to algebraic varieties. The geometry related to harmonic functions is discussed in detail.

Keywords:   Chevalley, Laplace equation, partial differential equations, algebraic varieties, compact

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