Discrete Wiener Algebra in the Bicomplex Setting, Spectral Factorization with Symmetry, and Superoscillations

TL;DR

This paper develops Wiener algebra theories in the bicomplex setting, linking bicomplex and complex analysis with symmetry, and applies these concepts to superoscillations, highlighting new mathematical connections and potential applications.

Contribution

It introduces parallel Wiener algebra theories in bicomplex analysis, establishing links to classical complex analysis with symmetry and applying them to superoscillation phenomena.

Findings

Bicomplex Wiener algebras can be connected to classical complex analysis with symmetry.

The paper provides a framework for spectral factorization in the bicomplex setting.

Application to superoscillations demonstrates practical relevance.

Abstract

In this paper we present parallel theories on constructing Wiener algebras in the bicomplex setting. With the appropriate symmetry condition, the bicomplex matrix valued case can be seen as a complex valued case and, in this matrix valued case, we make the necessary connection between classical bicomplex analysis and complex analysis with symmetry. We also write an application to superoscillations in this case.