An operator equation characterizing the Laplacian

Authors:
H. König and V. Milman

Original publication:
Algebra i Analiz, tom **24** (2012), nomer 4.

Journal:
St. Petersburg Math. J. **24** (2013), 631-644

MSC (2010):
Primary 47A62

DOI:
https://doi.org/10.1090/S1061-0022-2013-01257-X

Published electronically:
May 24, 2013

MathSciNet review:
3088010

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The Laplace operator on satisfies the equation

for all and . Assume, in addition, that is -invariant and annihilates the affine functions, and that is nondegenerate. Then is a multiple of the Laplacian on , and a multiple of the derivative,

No continuity or linearity requirement is imposed on or .

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Additional Information

**H. König**

Affiliation:
Mathematisches Seminar, Universität Kiel, 24098 Kiel, Germany

Email:
hkoenig@math.uni-kiel.de

**V. Milman**

Affiliation:
School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel

Email:
milman@post.tau.ac.il

DOI:
https://doi.org/10.1090/S1061-0022-2013-01257-X

Keywords:
Laplace operator,
second order Leibniz rule,
operator functional equations

Received by editor(s):
November 1, 2011

Published electronically:
May 24, 2013

Additional Notes:
Supported in part by the Alexander von Humboldt Foundation, by ISF grant 387/09, and BSF grant 2006079.

Article copyright:
© Copyright 2013
American Mathematical Society