Dear Colleagues,

You are most cordially invited to the seminar organized by the Department of Mathematics.

Speaker: Hakkı Turgay Kaptanoğlu (Bilkent University)

Title: Shift Operators on Hilbert Harmonic Function Spaces

Abstract: In an attempt to identify the harmonic Drury-Arveson space, we introduce and investigate large families of reproducing kernel Hilbert spaces of harmonic functions the unit ball of $\mathbb R^n$. Using zonal harmonics, we define and develop basic properties of shift operators and their adjoints in the harmonic setting. We prove a dilation result for the shift operators on harmonic spaces that are row contractions. As a consequence, we show that the norm of one of our spaces Ğ is maximal among those spaces on which the shift operator is a row contraction. We also show the maximality of the operator norm of the shift on Ğ among contractive Hilbert norms on harmonic polynomials. We then describe the progress towards a von Neumann inequality for harmonic polynomials and a tuple of commuting operators on harmonic spaces that are row contractions and belong to a certain class.

This presentation is based on joint works with Ebrahim Samei and Varvara Shepelska of University of Saskatchewan, Canada.

Date: Friday, October 18, 2019

Time: 13:00

Place: Seminar Room

Physics-Mathematics Seminar Room