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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

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

Author(s): Michael Schmuckenschläger
Journal: Proc. Amer. Math. Soc. 126 (1998), 1527-1530.
MSC (1991): Primary 52A20
MathSciNet review: 1425138
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Abstract | References | Similar articles | Additional information

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 $1/\sqrt{12}$.

References:

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K. Ball, Logarithmically Concave Functions and Sections of Convex Sets in $\mathbf R^n$, Studia Math. 88 (1988), 69-84. MR 89e:52002

[B2]
K. Ball, Normed Spaces with a weak Gordon Lewis Property, Proc. Funct. Anal., Univ. of Texas and Austin, 1987-1989, Springer LNM 1470, 36-47. MR 93e:46013

[C]
K. L. Chung, A Course in Probability Theory, Academic Press, 1974. MR 49:11579

[MeP]
M. Meyer and A. Pajor, Sections of the Unit Ball of $\ell _p^n$, J. Funct. Anal. 80 (1988), 109-123. MR 89h:52010

[MiP]
V. D. Milman and A. Pajor, Isotropic Position, Inertia Ellipsoids and Zonoids of the Unit Ball of an $n$-dimensional Normed Space, GAFA Seminar 87-89, Springer LNM 1376, 64-104. MR 90g:52003

[SS]
G. Schechtman and M. Schmuckenschläger, Another Remark on the Volume of the Intersection of Two $L_p^n$ Balls, GAFA 89/90, 174-178, Springer 1991. MR 92j:52008

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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: 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
Copyright of article: Copyright 1998, American Mathematical Society




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