An "inverse Fekete-Szegö problem" and filtration of generators

Fiana Jacobzon (Braude College of Engineering, Karmiel, Israel)

28-Jun-2022, 13:00-14:00 (21 months ago)

Abstract: In this talk we introduce and discuss a question that can be interpreted as an "inverse Fekete-Szegö problem". It turns out that this problem links to the so-called filtration of infinitesimal generators. Several filtration classes have recently been studied, including their applications to semigroups of holomorphic mappings in the unit disk. To address the circle of questions that arise in this context we introduce new filtration classes using the non-linear differential operator \[\alpha\cdot \frac{f(z)}{z}+\beta\cdot \frac{zf'(z)}{f(z)}+(1-\alpha-\beta)\cdot \left[1+\frac{zf''(z)}{f'(z)}\right],\] and establish certain properties of these classes. Sharp upper bounds of the modulus of the Fekete--Szegö functional over some filtration classes are found. We also present open problems for further study.

Joint work with Mark Elin (Braude College of Engineering, Karmiel, Israel) and Nikola Tuneski (Ss. Cyril and Methodius University, Skopje, Republic of North Macedonia)

complex variablesdynamical systems

Audience: researchers in the topic


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