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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Minkowski valuations on $ L^p$-spaces


Author: Andy Tsang
Journal: Trans. Amer. Math. Soc. 364 (2012), 6159-6186
MSC (2010): Primary 52A20; Secondary 46E30, 52B45
Published electronically: June 27, 2012
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Abstract: A complete classification is obtained of continuous $ \operatorname {GL}(n)$-
equivariant Minkowski valuations on $ L^p(\mathbb{R}^n,\vert x\vert dx)$. As a consequence, a characterization of the moment body for functions is obtained.


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Additional Information

Andy Tsang
Affiliation: Department of Mathematics, Polytechnic Institute of New York University, Six MetroTech Center, Brooklyn, New York 11201
Email: atsang122@verizon.net

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05681-9
PII: S 0002-9947(2012)05681-9
Received by editor(s): May 25, 2010
Published electronically: June 27, 2012
Additional Notes: This research was taken from the dissertation submitted to the Faculty of the Polytechnic Institute of New York University in partial fulfillment of the requirements for the degree Doctor of Philosophy (Mathematics), June 2010.
Article copyright: © Copyright 2012 American Mathematical Society