Phi-transform on domains

TL;DR

This paper develops a method to construct specialized frames on domains with smooth boundaries, enabling detailed analysis of Besov spaces for applications in signal processing and functional analysis.

Contribution

It introduces a new approach to create bandlimited, highly localized, and nearly tight frames on smooth boundary domains, facilitating Besov space characterization.

Findings

Frames are effectively constructed on smooth boundary domains.

The frames enable precise description of Besov spaces.

The method improves analysis tools for functions on complex domains.

Abstract

The goal of the present paper is to construct bandlimited highly localized and nearly tight frames on domains with smooth boundaries in Euclidean spaces. These frames are used do describe corresponding Besov spaces.