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 the 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.
|投稿的翻译标题||Delsarte method in the problem on kissing numbers in high-dimensional spaces|
|期刊||Труды института математики и механики УрО РАН|
|州||Published - 2012|
- 27.00.00 MATHEMATICS
Level of Research Output
- VAK List