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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Volume of intersections and sections
of the unit ball of $\ell _p^n$


Author: Michael Schmuckenschläger
Journal: Proc. Amer. Math. Soc. 126 (1998), 1527-1530
MSC (1991): Primary 52A20
MathSciNet review: 1425138
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Abstract: An asymptotic formula for the volume of the intersection of a suitable multiple of the unit ball of $\ell _p^n$ and the cube $[-1/2,1/2]^n$ will be proved. We also show that the isotropic constant of the unit ball of $\ell _n^p,\ 1\le p\le 2$, is bounded by $1/\sqrt{12}$.


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Additional Information

Michael Schmuckenschläger
Affiliation: Weizmann Institute of Science, Rehovot, Israel; Mathematisches Seminar, Universität Kiel, Germany; Institut für Mathematik, Universität Linz, Austria
Address at time of publication: Institut für Mathematik, J. Kepler Universität, A-4040 Linz, Austria
Email: schmucki@caddo.bayou.uni-linz.ac.at

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04179-3
PII: S 0002-9939(98)04179-3
Received by editor(s): June 14, 1996
Received by editor(s) in revised form: October 14, 1996
Additional Notes: The author was supported in part by BSF and Erwin Schrödinger Auslandsstipendium J0630, J0804
Communicated by: Dale Alspach
Article copyright: © Copyright 1998 American Mathematical Society