C. Boyd

will speak on

The Regular Radius of Convergence

Time: 3:00PM
Date: Tue 9th April 2024
Location: E0.32 (beside Pi restaurant) [map]

Further information

Abstract: We will begin by recalling the definition of a complex Banach lattice, regular homogeneous polynomial and the modulus, $|P_m|$, of a regular polynomial $P_m$. Given a Taylor series, $f=\sum_{m=0}^\infty P_m$, about $a$ in a complex Banach lattice $E$ with each $P_m$ a regular $m$-homogeneous polynomial we define the radius of regular convergence of $f$, $|r|(f,a)$, as the supremium of $\rho>0$ such that $\sum_{m=0}^\infty|P_m|$ converges on $B(a,\rho)$. We extend the definition of homogeneous Bohr radius of Defant, Garc{\'\i}a and Maestre to Banach lattice and see how these radii determine a lower bound for the ratio between the radius
of regular convergence and the (standard) radius of convergence. This allows us to determine the radius of regular convergence for specific Banach lattices and uncover the relationship between Taylor series and monomial convergence
on Banach spaces with an unconditional basis.


This is joint work with R. Ryan and N. Snigireva.


https://ucd-ie.zoom.us/j/67395313846

(This talk is part of the Analysis series.)

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