Explicit commutative sequence space representations of function and distribution spaces on the real half-line

TL;DR

This paper introduces explicit sequence space models for classical function and distribution spaces on the real half-line using Fourier transforms of wavelet basis elements, facilitating better analysis and understanding.

Contribution

It provides a novel explicit representation of function and distribution spaces via sequence spaces based on wavelet Fourier transforms, enhancing analytical tools.

Findings

Explicit sequence space representations for function spaces.

Representation of distribution spaces using wavelet Fourier transforms.

Facilitates analysis of classical spaces on the real half-line.

Abstract

We provide explicit commutative sequence space representations for classical function and distribution spaces on the real half-line. This is done by evaluating at the Fourier transforms of the elements of an orthonormal wavelet basis.