Thu Hien Nguyen, Julius Maximilian University of Wurzburg

will speak on

Analytic closure of sets of hyperbolic polynomials and hyperbolicity preservers

Time: 3:00PM
Date: Tue 19th November 2024
Location: E0.32 (beside Pi restaurant) [map]

Further information

Abstract: The Laguerre--P\'olya class is a special class of entire
functions that are locally the limit of sequences of real univariate hyperbolic polynomials. We present some necessary and sufficient conditions for entire functions to belong to the Laguerre--P\'olya class, or to have no complex roots. These conditions involve only their Taylor coefficients, therefore, are easy to apply. For an entire function $f(z)
= \sum_{k=0}^{\infty} a_k z^k$, we define the second quotients of Taylor coefficients as $q_n(f) := \frac{a_{n-
1}^2}{a_{n-2} a_{n}}$, $n\geq 2$, and formulate the
conditions in terms of $q_n(f)$. We also discuss the
operators that preserve real-rootedness.

This is joint work with Anna Vishnyakova.

https://ucd-ie.zoom.us/j/66840518903

(This talk is part of the Analysis series.)

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