Delsarte Method in the Problem on Kissing Numbers in High-Dimensional Spaces

被引：3

作者：

Kuklin, N. A. ^{[1
,2
]}

机构：

[1] Ural Fed Univ, Inst Math & Comp Sci, Ekaterinburg 620000, Russia

[2] Russian Acad Sci, Ural Branch, Inst Math & Mech, Ekaterinburg 620990, Russia

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2014年 / 284卷

基金：

俄罗斯基础研究基金会;

关键词：

Delsarte method; infinite-dimensional linear programming; Gegenbauer polynomials; kissing numbers; ALGORITHM; BOUNDS;

D O I：

10.1134/S0081543814020102

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider extremal problems for continuous functions that are nonpositive on a closed interval and can be represented as series in Gegenbauer polynomials with nonnegative coefficients. These problems arise from the Delsarte method of finding an upper bound for the kissing number in a Euclidean space. We develop a general method for solving such problems. Using this method, we reproduce results of previous authors and find a solution in the following 11 new dimensions: 147, 157, 158, 159, 160, 162, 163, 164, 165, 167, and 173. The arising extremal polynomials are of a new type.

引用

页码：S108 / S123

页数：16

共 50 条

[1] Delsarte method in the problem on kissing numbers in high-dimensional spaces
Kuklin, N. A.
TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2012, 18 (04): : 224 - 239
[2] Delsarte method in the problem on kissing numbers in high-dimensional spaces
N. A. Kuklin
Proceedings of the Steklov Institute of Mathematics, 2014, 284 : 108 - 123
[3] Constructive Kissing Numbers in High-Dimensional Spaces
Lanju Xu
Journal of Systems Science and Complexity, 2007, 20 : 30 - 40
[4] Constructive kissing numbers in high-dimensional spaces
Xu, Lanju
JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY, 2007, 20 (01) : 30 - 40
[5] ON THE PROBLEM OF VISUALIZING POINT-DISTRIBUTIONS IN HIGH-DIMENSIONAL SPACES
BECKMANN, PE
COMPUTERS & GRAPHICS, 1995, 19 (04) : 617 - 629
[6] The extremal function in the Delsarte problem of finding an upper bound for the kissing number in the three-dimensional space
N. A. Kuklin
Proceedings of the Steklov Institute of Mathematics, 2015, 288 : 99 - 111
[7] EM in high-dimensional spaces
Draper, BA
Elliott, DL
Hayes, J
Baek, K
IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS, 2005, 35 (03): : 571 - 577
[8] The mathematics of high-dimensional spaces
Rogers, D
ABSTRACTS OF PAPERS OF THE AMERICAN CHEMICAL SOCIETY, 1998, 215 : U524 - U524
[9] The extremal function in the Delsarte problem of finding an upper bound for the kissing number in the three-dimensional space
Kuklin, N. A.
TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2014, 20 (01): : 130 - 141
[10] The Extremal Function in the Delsarte Problem of Finding an Upper Bound for the Kissing Number in the Three-Dimensional Space
Kuklin, N. A.
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2015, 288 : S99 - S111

← 1 2 3 4 5 →