Vol. 303, No. 2, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 310: 1
Vol. 309: 1  2
Vol. 308: 1  2
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Polarization, sign sequences and isotropic vector systems

Gergely Ambrus and Sloan Nietert

Vol. 303 (2019), No. 2, 385–399

We determine the order of magnitude of the n-th p-polarization constant of the unit sphere Sd1 for every n,d 1 and p > 0. For p = 2, we prove that extremizers are isotropic vector sets, whereas for p = 1, we show that the polarization problem is equivalent to that of maximizing the norm of signed vector sums. Finally, for d = 2, we discuss the optimality of equally spaced configurations on the unit circle.

PDF Access Denied

However, your active subscription may be available on Project Euclid at

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

polarization problems, discrete potentials, Chebyshev constants, isotropic vectors sets, tight frames, vector sums
Mathematical Subject Classification 2010
Primary: 52A40
Secondary: 41A17
Received: 23 April 2019
Revised: 19 June 2019
Accepted: 19 June 2019
Published: 4 January 2020
Gergely Ambrus
Alfréd Rényi Institute of Mathematics
Hungarian Academy of Sciences
Sloan Nietert
Department of Computer Science
Cornell University
Ithaca, NY
United States