Bicomplex Weighted Hardy Spaces and Bicomplex C*-algebras

TL;DR

This paper explores bicomplex weighted Hardy spaces, introduces bicomplex C*-algebras, and generalizes classical Hardy space results, providing new insights into their structure and properties.

Contribution

It introduces the concept of bicomplex C*-algebras and extends classical Hardy space results to the bicomplex setting.

Findings

Reproducing kernels for bicomplex weighted Hardy spaces are characterized.

Generalization of classical Hardy space results to the bicomplex context.

Properties of bicomplex C*-algebras, including maximal ideals, are discussed.

Abstract

In this paper we study the bicomplex version of weighted Hardy spaces. Further, we describe reproducing kernels for the bicomplex weighted Hardy spaces. In particular, we generalize some results which holds for the classical weighted Hardy spaces. We also introduce the notion of bicomplex C*-algebra and discuss some of its properties including maximal ideals in BC.