Work

On the existence of an extremal function for the Delsarte extremal problem

Year: 2025

Type: article

Abstract: In the general setting of a locally compact Abelian group G, the Delsarte extremal problem asks for the supremum of integrals over the collection of continuous positive definite functions $$f \colon G \to \mathbb{R}$$ f : G → R satisfying $$f(0) = 1$$ f ( 0 ) = 1 and having $$supp f_{+} \subset \Omega$$ s u p p f + ⊂ Ω for some measurable subset $$\Omega$$ Ω of finite measure. In this paper, we consider the question of the existence of an extremal function for the Delsarte extremal problem. In particular, we show that there exists an extremal function for the Delsarte problem when $$\Omega$$ Ω is closed, extending previously known existence results to a larger class of functions.

Source: Analysis Mathematica

DOI: 10.1007/s10476-025-00072-x

Author: M. D. Ramabulana

Institution: University of Cape Town

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: University of Cape Town