Seminar za Analizu, 14. oktobar 2021.

• 11. Oktobar,  2021
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Naredni sastanak Seminara biće održan onlajn u četvrtak, 14. oktobra 2021. sa početkom u 15 časova preko Zoom platforme.

Predavač: Dragan Vukotić, Universidad Autónoma de Madrid, Spain

Naslov predavanja: THE HILBERT MATRIX OPERATOR ACTING ON SPACES OF ANALYTIC FUNCTIONS

Apstrakt:
The Hilbert matrix is an infinite matrix whose action on the space of square summable sequences induces a bounded linear operator. It is a most typical example of a Hankel operator whose norm can be determined by applying the well-known Hilbert inequality. It is possible to go well beyond the norm computation: the spectrum of the Hilbert matrix on the space of square summable sequences is well understood. We will cover briefly the early results on this from the 1950s.

The Hilbert matrix also induces a bounded operator on  other sequence spaces and on various spaces of analytic functions (including certain Hardy and Bergman spaces, Dirichlet-type spaces, as well as Korenblum-type growth spaces) but this has only been noticed in the last 20 years. We will review these more recent developments, including norm computations on different spaces and several other recent results regarding the spectrum of the induced operator.

Part of this talk is based on a joint work in progress with A. Aleman and A. Siskakis.

Link za pristup predavanju:
https://us02web.zoom.us/j/6636215428?pwd=bllJSTUvZ0E5MjhkMkxYa3RYYzZpQT09
Meeting ID: 663 621 5428
Passcode: 7h6KR1

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