Ekvationer
Seminarium i matematik

A brief introduction to Quantum Harmonic Analysis

Välkommen till föreläsningen i seminarieserien i matematik.

In this talk, we will give a brief introduction to the concepts of Quantum Harmonic Analysis (QHA). We discuss the concepts of function-operator and operator-operator convolutions as introduced by R. Werner in his 1984 paper “Quantum harmonic analysis on phase space”, as well as Werner’s concept of Correspondence Theory. This theory has, in the last years, turned out as a very efficient tool for operator theory. We will try to demonstrate this for operators acting on L2(R). As an application, we will discuss two results on pseudodifferential operators – namely the Calder ́on-Vaillancourt theorem and Cordes’ theorem on Heisenberg-smooth operators – from the QHA perspective.

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