Lecture Details
Name: Daniela Mariz Silva Vieira (USP - Universidade de São Paulo)Speaking: Thu 9th May 15:30 - 15:55Title: Spaceability, algebrability and residuality on some sets of analytic functions.Abstract: In this talk we will present results of the articles [1, 2], where we investigate different classes of analytic functions. We show that the subset of the disk algebra of the functions that are not in some Dales-Davie algebra is spaceable, strongly $\mathfrak{c}$-algebrable and residual in the disk algebra. We also show that the set of analytic functions from $\mathbb{C}^2$ into $\mathbb{C}^2$, which are not Lorch-analytic is spaceable and strongly $\mathfrak{c}$-algebrable, but is not residual in the space of entire functions from $\mathbb{C}^2$ into $\mathbb{C}^2$.
References
[1] M. L. Lourenço and D. M. Vieira, Algebrability of some subsets of the disk algebra, Bull. Belg. Math. Soc. Simon Stevin 23 (2016) 505-514.
[2] M. L. Lourenço and D. M. Vieira, Strong Algebrability and Residuality on Certain Sets of Analytic Functions, to appear Rocky Mountain Journal of Mathematics, 2019.