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On the Approximation of Positive Definite Functions With Compact Support by Smooth Functions

Year: 2024

Type: article

Abstract: In this paper we study a problem on approximation of continuous positive definite functions on R𝑛 with fixed value at the origin whose support is contained in a centrally symmetric convex body 𝐴 (the class F𝐴(R𝑛)) by smooth functions from the same class F𝐴(R𝑛). We prove that if 𝜙 ∈ F𝐴(R𝑛), then for every 𝜀 > 0 there is 𝜓 ∈ F𝐴(R𝑛) ∩ 𝐶∞(R𝑛) such that ‖𝜙 − 𝜓‖∞ < 𝜀.Keywords: positive-definite functions, extremal problems, Fourier transform.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.13752207

Author: Manov, A. D.

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W6893121023

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