On Monogenic Reproducing Kernel Hilbert Spaces of the Paley-Wiener Type

TL;DR

This paper develops and characterizes three types of reproducing kernel Hilbert spaces of Paley-Wiener type within Clifford algebra, providing spectrum descriptions, representation formulas, and kernel estimates.

Contribution

It introduces new Clifford algebra-based Paley-Wiener, Hardy, and Bergman spaces with detailed spectral and kernel characterizations.

Findings

Spectrum characterizations of the spaces

Representation formulas for functions

Estimates of reproducing kernels

Abstract

In the Clifford algebra setting the present study develops three reproducing kernel Hilbert spaces of the Paley-Wiener type, namely the Paley-Wiener spaces, the Hardy spaces on strips, and the Bergman spaces on strips. In particular, we give spectrum characterizations and representation formulas of the functions in those spaces and estimation of their respective reproducing kernels.