We consider an extremal problem for continuous functions that are nonpositive on a closed interval and can be represented by series in Legendre polynomials with nonnegative coefficients. This problem arises from the Delsarte method of finding an upper bound for the kissing number in the three-dimensional Euclidean space. We prove that the prolem has a unique solution, which is a polynomial of degree . This polynomial is a linear combination of Legendre polynomials of degrees with positive coefficients; it has simple root and five roots of multiplicity in . Also we consider dual problem for nonnegative measures on . We prove that extremal measure is unique.
|Título traduzido da contribuição||The extremal function in the Delsarte problem of finding an upper bound for the kissing number in the three-dimensional space|
|Revista||Труды института математики и механики УрО РАН|
|Número de emissão||1|
|Estado da publicação||Published - 2014|
Level of Research Output
- VAK List