Bicomplex Bergman spaces on bounded domains

TL;DR

This paper investigates bicomplex Bergman spaces on bounded domains, deriving their kernels from complex projections and introducing related reproducing kernel Hilbert spaces to expand understanding of bicomplex analysis.

Contribution

It computes the Bergman kernel for bicomplex domains using complex projections and introduces two new related reproducing kernel Hilbert spaces.

Findings

Bicomplex Bergman kernels expressed via complex projections

Introduction of two new reproducing kernel Hilbert spaces

Relations established between kernels of different spaces

Abstract

The bicomplex Bergman spaces are studied for any bounded bicomplex domain. Its Bergman kernel is computed in terms of the kernels of the complex projections of the domain. We also introduce two additional reproducing kernel Hilbert spaces and relate its kernels to that of the bicomplex Bergman space.