Universal Taylor Series on products of planar domains
Complex Variables
2019-09-10 v1 Classical Analysis and ODEs
Functional Analysis
Abstract
Using a recent Mergelyan type theorem for products of planar compact sets we establish generic existence of Universal Taylor Series on products of planar simply connected domains Omegai, i=1, . . . , d. The universal approximation is realized by partial sums of the Taylor development of the universal function on products of planar compact sets Ki, i=1, . . . , d such that the complement of Ki is connected and for at least one i0 the set Ki0 is disjoint from Omegai0.
Keywords
Cite
@article{arxiv.1909.03521,
title = {Universal Taylor Series on products of planar domains},
author = {K. Kioulafa and G. Kotsovolis and V. Nestoridis},
journal= {arXiv preprint arXiv:1909.03521},
year = {2019}
}