Daniel Seco ( Universidad Carlos III de Madrid)

will speak on

ZEROS OF OPTIMAL POLYNOMIAL APPROXIMANTS IN $\ell^p_A$

Time: 3:00PM
Date: Tue 2nd November 2021
Location: Seminar Room SCN 1.25 [map]

Further information

Abstract: The study of inner and cyclic functions in $l^p_A$ spaces
requires a better understanding of the zeros of so-called optimal polynomial approximants. We determine that a point of the complex plane is the zero of an optimal polynomial approximant for some element of $l^p_A$ if and only if it lies outside of a closed disk (centered at the origin) of a particular radius which depends on the value of p. We find the value of this radius for $p\not= 2$. In addition, for each positive integer $d$ there is a polynomial $f_d$ of degreeat most $d$ that minimizes the modulus of the root of its optimal linear polynomial approximant. We develop a method for finding these extremal functions $f_d$ and discuss their properties. The method involves the Lagrange multiplier method and a resulting dynamical system. This is a joint work with R. Cheng and W.Ross.



https://ucd-ie.zoom.us/j/63862034166?pwd=R0ZwK21FVC9DVVRUTU1PckNjUVRFQT09

(This talk is part of the Analysis series.)

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