Uncertainty Principles for Kac Algebras

TL;DR

This paper extends uncertainty principles to unimodular Kac algebras, characterizing minimizers and proving Hardy's principle using biprojections in subfactor theory.

Contribution

It introduces bi-shift of biprojections in Kac algebras and characterizes minimizers for key uncertainty principles, advancing the mathematical understanding of non-commutative harmonic analysis.

Findings

Characterization of minimizers for Hirschman-Beckner and Donoho-Stark principles.

Proof of Hardy's uncertainty principle in the context of unimodular Kac algebras.

Introduction of bi-shift biprojections in subfactor theory.

Abstract

In this paper, we introduce the notation of bi-shift of biprojections in subfactor theory to unimodular Kac algebras. We characterize the minimizers of Hirschman-Beckner uncertainty principle and Donoho-Stark uncertainty principle for unimodular Kac algebras with biprojections and prove Hardy's uncertainty principle in terms of minimizers.