Duality for Delsarte's extremal problem on compact Gelfand pairs

Summary · qwen2.5:32b

The study explores Delsarte-type extremal problems for positive definite functions on compact Gelfand pairs using infinite-dimensional linear programming, with implications for Turán and Delsarte problems in number theory, sphere packing, and statistics. The paper establishes and proves a strong duality statement for these problems. Notably, the research includes compact Abelian groups as a specific case.

Suggested post angle

Exploring the Duality for Delsarte's extremal problem on compact Gelfand pairs in mathematics.

Excerpt

arXiv:2603.11792v4 Announce Type: replace Abstract: We study Delsarte-type problems for positive definite functions on compact Gelfand pairs as infinite-dimensional linear programming problems. This setup includes, as a particular case, the case of compact Abelian groups. Depending on the restriction on the signs of the functions, we obtain two important particular cases, the Tur\'an and Delsarte problems. These problems have been studied in relation to number theory, sphere packing, and statistics. In this paper, we describe their duals and prove a strong duality statement.