Analysis Seminar

Artur Płaneta, Agricultural University of Krakow

"Conjugations in L2 spaces on the unit circle and the real line"

One of the axioms of standard quantum theory requires that the Hamiltonian H, which is the operator that expresses the dynamics of the quantum system, be Hermitian. However, this requirement is mathematical rather than physical in character. One possibility to replace this requirement is to consider the conjugation PT and PT symmetries.

In this talk, we will give an overview of recent research of conjugations on real line and unit circle. We will mainly focus on conjugations which have similar properties as PT with respect to multiplication operators and translations. We will also discuss the relationship between conjugations, model spaces, and Toeplitz kernels.

This seminar will be held jointly online and in person:

• Zoom link: https://us02web.zoom.us/j/87274747278?pwd=RG1Bak5lbk1GaHdIL0dtSzlBbjdiUT09
• Room: MC 5501