Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Sidel'nikov inequality

Authors: N. O. Kotelina and A. B. Pevnyĭ
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 26 (2014), nomer 2.
Journal: St. Petersburg Math. J. 26 (2015), 351-356
MSC (2010): Primary 26D15
Published electronically: February 3, 2015
MathSciNet review: 3242039
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The Sidel'nikov integral inequality was established in 1974 with a very difficult proof. A discrete version of this inequality was studied by Goethals and Seidel (1979) and by B. B. Venkov (2001). They found certain conditions under which equality occurs in the discrete inequality. In the paper, a simple proof of the Sidel'nikov inequality is suggested, based on an idea of Venkov.

References [Enhancements On Off] (What's this?)

  • 1. V. M. Sidel'nikov, New estimates for the closest packing of spheres in $ n$-dimensional Euclidean space, Mat. Sb. 95 (1974), no. 1, 148-158; English transl., Sb. Math. 24 (1974), no. 1, 147-157. MR 0362060 (50:14502)
  • 2. P. G. Casazza, Custom building finite frames, Wavelets, Frames and Operator Theory, Contemp. Math., vol. 345, Amer. Math., Soc., Providence, RI, 2004, pp. 68-86. MR 2066822 (2005f:42078)
  • 3. N. O. Kotelina and A. B. Pevnyĭ, Extremal properties of spherical half-designs, Algebra i Analiz 22 (2010), no. 5, 131-139; English transl., St. Petersburg Math. J. 22 (2011), no. 5, 795-801. MR 2828829 (2012e:05048)
  • 4. J. M. Goethals and J. J. Seidel, Spherical designs, Proc. Sympos. Pure Math., vol. 34, Amer. Math. Soc., Providence, RI, 1979. MR 525330 (82h:05014)
  • 5. B. Reznick, Sums of even powers of real linear forms, Mem. Amer. Math. Soc. 96 (1992), no. 463. MR 1096187 (93h:11043)
  • 6. B. Venkov, Réseaux et designs sphériques, Réseaux Euclidiens, Designs Sphériques et Formes Modulaires, Monogr. Enseign. Math., vol. 37, Enseignment Math., Genève, 2001, 10-86. MR 1878745 (2002m:11061)
  • 7. P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geom. Dedicata 6 (1977), no. 3, 363-388. MR 0485471 (58:5302)

Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2010): 26D15

Retrieve articles in all journals with MSC (2010): 26D15

Additional Information

N. O. Kotelina
Affiliation: Syktyvkar State University, Oktyabr′skiĭ pr. 55, Syktyvkar 167001, Russia

A. B. Pevnyĭ
Affiliation: Syktyvkar State University, Oktyabr′skiĭ pr. 55, Syktyvkar 167001, Russia

Keywords: Sidel{\textprime}nikov inequality, spherical semidesign
Received by editor(s): December 24, 2012
Published electronically: February 3, 2015
Article copyright: © Copyright 2015 American Mathematical Society

American Mathematical Society