On Delsarte-type extremal problems for positive definite functions

Ramabulana, Mita Dimpho

On Delsarte-type extremal problems for positive definite functions

Thesis / Dissertation

2026

Publisher

University of Cape Town

Department

Department of Mathematics and Applied Mathematics

Faculty

Faculty of Science

Abstract

This thesis considers Delsarte-type extremal problems for positive definite functions on locally compact Abelian groups and homogeneous spaces. It is shown, under general conditions, that an extremal function exists for very general Delsarte-type extremal problems on locally compact Abelian groups. We also attempt to unify different formulations of the extremal problem and study the extent to which these formulations are equivalent. Finally, we consider the Tur´an problem for spherical caps on the sphere, which we generalise to homogeneous spaces and show the existence of an extremal function.

Keywords

Mathematics

Reference:

Collections

PhD / Doctoral

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