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V. Nestoridis

Publications and source records attributed to V. Nestoridis.

At least 19 recordsLinked to original sources
arXiv2022

Double algebraic genericity of universal harmonic functions on trees in the general case

It has been shown that the set of universal functions on trees contains a linear subspace except zero, dense in the space of harmonic functions. In this paper we show that the set of universal functions contains two linear subspaces except zero, dense in the space of harmonic functions that intersect only at zero. We work in the most general case that has been studied so far, letting our functions take values over a topological vector space.

math.FA↗
arXiv2020

Generalized Harmonic Functions on Trees: Universality and Frequent Universality

Recently, harmonic functions and frequently universal harmonic functions on a tree $T$ have been studied, taking values on a separable Fréchet space $E$ over the field $\mathbb{C}$ or $\mathbb{R}$. In the present paper, we allow the functions to take values in a vector space $E$ over a rather general field $\mathbb{F}$. The metric of the separable topological vector space $E$ is translation invariant and instead of harmonic functions we can also study more general functions defined by linear combinations with coefficients in $\mathbb{F}$. Unlike the past literature, we don't assume that $E$ is complete and therefore we present a new argument, avoiding Baire's theorem.

math.FA↗
arXiv2019

Universal Taylor Series on products of planar domains

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.

math.CV↗
arXiv2019

Algebraic genericity of frequently universal harmonic functions on trees

We show that the set of frequently universal harmonic functions on a tree T contains a vector space except 0 which is dense in the space of harmonic functions on T seen as subset of C^T . In order to prove this we replace the complex plane C by any separable Frechet space E and we repeat all the theory.

math.FA↗
arXiv2018

Generic non-extendability and total unboundedness in function spaces

For a function space $X(\OO)$ satisfying weak assumptions we prove that the generic function in $X(\OO)$ is totally unbounded, hence non-extendable. We provide several examples of such spaces; they are mainly localized versions of classical function spaces and intersections of them.

math.CV↗
arXiv2018

Jordan domains with a rectifiable arc in their boundary

We show that if an open arc J of the boundary of a Jordan domain $Ω$ is rectifiable, then the derivative $Φ$' of the Riemann map $Φ: D\rightarrow Ω$ from the open unit disk D onto $Ω$ behaves as an $H^1$ function when we approach the arc $Φ^{-1}(J^{\prime})$,where $J^{\prime}$ is any compact subarc of $J$. "

math.CV↗
arXiv2018

One sided extendability and p-continuous analytic capacities

Using complex methods combined with Baire's Theorem we show that one-sided extendability, extendability and real analyticity are rare phenomena on various spaces of functions in the topological sense. These considerations led us to introduce the p-continuous analytic capacity and variants of it, $p \in \{ 0, 1, 2, \cdots \} \cup \{ \infty \}$, for compact or closed sets in $\mathbb{C}$. We use these capacities in order to characterize the removability of singularities of functions in the spaces $A^p$.

math.CV↗
arXiv2017

Open, convex, unbounded sets in normed spaces

Let X be a normed linear space. We examine if every open, convex and unbounded subset of X is equal to the union of a family of open straight half lines. The answer is affirmative if and only if X is finite dimensional.

math.FA↗
arXiv2017

Non-extendability of holomorphic functions with bounded or continuously extendable derivatives

We consider the spaces $H_{F}^{\infty}(Ω)$ and $\mathcal{A}_{F}(Ω)$ containing all holomorphic functions $f$ on an open set $Ω\subseteq \mathbb{C}$, such that all derivatives $f^{(l)}$, $l\in F \subseteq \mathbb{N}_0=\{ 0,1,...\}$, are bounded on $Ω$, or continuously extendable on $\overlineΩ$, respectively. We endow these spaces with their natural topologies and they become Fréchet spaces. We prove that the set $S$ of non-extendable functions in each of these spaces is either void, or dense and $G_δ$. We give examples where $S=\varnothing$ or not. Furthermore, we examine cases where $F$ can be replaced by $\widetilde{F}=\{ l\in \mathbb{N}_0:\min F \leqslant l \leqslant \sup F\}$, or $\widetilde{F}_0= \{ l\in \mathbb{N}_0:0\leqslant l \leqslant \sup F\}$ and the corresponding spaces stay unchanged.

math.CV↗
arXiv2017

Domains of Holomorphy

We give a simple and more elementary proof that the notions of Domain of Holomorphy and Weak Domain of Holomorphy are equivalent. This proof is based on a combination of Baire's Category Theorem and Montel's Theorem. We also obtain generalizations by demanding that the non-extentable functions belong to a particular class of holomorphic functions in the domain. We give an example of a domain in the plane which is a domain of holomorphy with respect to the class of all holomorphic functions but not with respect to the class of holomorphic functions continuously extendable on the closure of the domain.

math.CV↗
arXiv2017

On Bergman type spaces of holomorphic functions and the density, in these spaces, of certain classes of singular functions

We consider Bergman spaces and variations of them in one or several complex variables. For some domains we show that in these spaces the generic function is totally unbounded and hence non - extendable. We also show that the generic function is not - even locally - in Bergman spaces of higher order. Finally, in certain domains we consider the space of holomorphic functions whose derivatives up to some order extend continuously to the closure of the domain endowed with its natural topology. Generically, every function in this space is proven to be non - extendable, although bounded.

math.CV↗
arXiv2016

One sided conformal collars and the reflection principle

If a Jordan curve σ has a one-sided conformal collar with "good" properties, then, using the Reflection principle, we show that any other conformal collar of σ from the same side has the same "good" properties. A particular use of this fact concerns analytic Jordan curves, but in general the Jordan arcs we consider do not have to be analytic. We show that if an one-sided conformal collar bounded by σ is of class A^p, then any other collar bounded by σ and from the same side of σ is of class A^p.

math.CV↗
arXiv2016

One valued primitives and the F. and M. Riesz theorem

For a non-simply connected domain Omega in C and f a holomorphic function on Omega we prove that f admits one-valued primitives of any order in Omega, if and only if, it extends holomorphically in the simply connected envelope of Omega . This leads to a generalization of the F. and M. Riesz theorem.

math.CV↗
arXiv2015

Simultaneous Universal Padé Approximation

We prove simultaneous universal Padé approximation for several universal Padé approximants of several types. Our results are generic in the space of holomorphic functions, in the space of formal power series as well as in a subspace of $A^{\infty}$. These results are valid for one center of expansion or for several centers as well.

math.CV↗
arXiv2015

Universal Padé approximants on simply connected domains

The theory of universal Taylor series can be extended to the case of Padé approximants where the universal approximation is not realized by polynomials any more, but by rational functions, namely the Padé approximants of some power series. We present the first generic result in this direction, for Padé approximants corresponding to Taylor developments of holomorphic functions in simply connected domains. The universal approximation is required only on compact sets $K$ which lie outside the domain of definition and have connected complement. If the sets $K$ are additionally disjoint from the boundary of the domain of definition, then the universal functions can be smooth on the boundary.

math.CV↗