Abstract
We express the volume of central hyperplane sections of star bodies inR n in terms of the Fourier transform of a power of the radial function, and apply this result to confirm the conjecture of Meyer and Pajor on the minimal volume of central sections of the unit balls of the spacesℓ n p with 0<p<2.
Similar content being viewed by others
References
K. Ball,Cube slicing in ℝn, Proceedings of the American Mathematical Society97 (1986), 465–473.
R. J. Gardner,Geometric Tomography, Cambridge University Press, Cambridge, 1995.
I. M. Gelfand and G. E. Shilov,Generalized Functions 1. Properties and Operations, Academic Press, New York, 1964.
S. Helgason,The Radon Transform, Birkhäuser, Boston, 1980.
A. Koldobsky,Schoenberg’s problem on positive definite functions (English translation in St. Petersburg Mathematical Journal3 (1992), 563–570), Algebra and Analysis3 (1991), 78–85.
A. Koldobsky,Characterization of measures by potentials, Journal of Theoretical Probability7 (1994), 135–145.
M. Meyer and A. Pajor,Sections of the unit ball of ℓ n p , Journal of Functional Analysis80 (1988), 109–123.
V. M. Zolotarev,One-Dimensional Stable Distributions, American Mathematical Society, Providence, 1986.
Author information
Authors and Affiliations
Corresponding author
Additional information
Research supported in part by the NSF Grant DMS-9531594.
Rights and permissions
About this article
Cite this article
Koldobsky, A. An application of the fourier transform to sections of star bodies. Isr. J. Math. 106, 157–164 (1998). https://doi.org/10.1007/BF02773465
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02773465