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A note on isoparametric polynomials

A note on isoparametric polynomials We show that any homogeneous polynomial solution of the eiconal type equation $$|\nabla F(x)|^2=m^2|x|^{2m-2}$$ | ∇ F ( x ) | 2 = m 2 | x | 2 m - 2 , $$m\ge 1$$ m ≥ 1 , is either a radially symmetric polynomial $$F(x)=\pm |x|^{m}$$ F ( x ) = ± | x | m (for even $$m$$ m ’s) or it is a composition of a Chebychev polynomial and a Cartan–Münzner polynomial. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

A note on isoparametric polynomials

Analysis and Mathematical Physics , Volume 4 (3) – Jan 14, 2014

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References (22)

Publisher
Springer Journals
Copyright
Copyright © 2014 by Springer Basel
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-014-0067-z
Publisher site
See Article on Publisher Site

Abstract

We show that any homogeneous polynomial solution of the eiconal type equation $$|\nabla F(x)|^2=m^2|x|^{2m-2}$$ | ∇ F ( x ) | 2 = m 2 | x | 2 m - 2 , $$m\ge 1$$ m ≥ 1 , is either a radially symmetric polynomial $$F(x)=\pm |x|^{m}$$ F ( x ) = ± | x | m (for even $$m$$ m ’s) or it is a composition of a Chebychev polynomial and a Cartan–Münzner polynomial.

Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Jan 14, 2014

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