arXiv subjects

Georgios Nikolaidis

Publications and source records attributed to Georgios Nikolaidis.

8 recordsLinked to original sources

arXiv2026

Loewner chains with multiple boundary attraction points: A construction via close-to-convex functions

In this work we construct multi-slit \textit{chordal Loewner chains} with multiple attraction points on the real line. We build a model domain with the use of close-to-convex functions, in a way that allow us to prescribe the attraction points. These families of Loewner chains resemble the classical model for semigroups of holomorphic maps of the upper half-plane. Our work is to choose an appropriate set of arbitrarily many parameters and to study the geometric behavior of the model domain, as it evolves with respect to time, in order to derive the aforementioned Loewner chain. Finally, with the use of harmonic measure, we calculate the angles of convergence of each slit of the chain.

math.CV↗

arXiv2025

Fractional Volterra-type operator induced by radial weight acting on Hardy space

Given a radial doubling weight $\mu$ on the unit disc $\mathbb{D}$ of the complex plane and its odd moments $\mu_{2n+1}=\int_0^1 s^{2n+1}\mu(s)\, ds$, we consider the fractional derivative $$ D^\mu(f)(z)=\sum_{n=0}^{\infty} \frac{\widehat{f}(n)}{\mu_{2n+1}}z^n, $$ of a function $ f(z)=\sum_{n=0}^{\infty}\widehat{f}(n)z^n$ analytic in $\mathbb{D}$. We also consider the fractional integral operator $I^\mu(f)(z)=\sum_{n=0}^{\infty} \mu_{2n+1}\widehat{f}(n)z^n$, and the fractional Volterra-type operator $$ V_{\mu,g}(f)(z)= I^\mu(f\cdot D^\mu(g))(z),\quad f\in\mathcal{H}(\mathbb{D}), $$ for any fixed $g\in\mathcal{H}(\mathbb{D})$. We prove that $V_{\mu,g}$ is bounded (compact) on a Hardy space $H^p$, $0<p<\infty$, if and only if $g$ belongs to $\text{BMOA}$ ($\text{VMOA}$). Moreover, if $\int_0^1 \frac{\left(\int_r^1 \mu(s)\, ds\right)^p}{(1-r)^2}\,dr=+\infty$, we prove that $V_{\mu,g}$ belongs to the Schatten class $S_p(H^2)$ if and only if $g=0$. On the other hand, if $\frac{\left(\int_r^1 \mu(s)\, ds\right)^p}{(1-r)^2}$ is a radial doubling weight it is proved that $V_{\mu,g} \in S_p(H^2)$ if and only if $g$ belongs to the Besov space $B_p$. En route, we obtain descriptions of $H^p$, $\text{BMOA}$, $\text{VMOA}$ and $B_p$ in terms of the fractional derivative $D^\mu$.

math.CV↗

arXiv2025

Trace ideal criteria for generalized integration operators

For $g \in \operatorname{Hol}(\mathbb D)$, we study the class of generalized integration operators $T_{g,a}$, acting on Hardy and Bergman spaces of the unit disc in the complex plane. This class of integral operators were introduced to study factorization theorems in the Hardy spaces of the unit disc. We completely characterize the space of symbols g, for which $T_{g,a}$ belongs to the Schatten-von Neumann ideals of the Hardy and Bergman spaces.

math.CV↗

arXiv2024

Meromorphic Optimal domain of Integral Operators

For $g\in BMOA$, we introduce the meromorphic optimal domain $(T_g,H^p)$, i.e. the space containing the meromorphic functions that are mapped under the action of the generalized Volterra operator $T_g$ into the Hardy space $H^p$. We investigate its properties and characterize for which $g_1,g_2 \in BMOA$ the corresponding meromorphic optimal domains coincide. This investigation contributes to a more comprehensive understanding of the holomorphic optimal domain of $T_g$ in $H^p$.

math.CV↗

arXiv2024

On the boundedness of generalized integration operators on Hardy spaces

We study the boundedness and compactness properties of the generalized integration operator $T_{g,a}$ when it acts between distinct Hardy spaces in the unit disc of the complex plane. This operator has been introduced by the first author in connection to a theorem of Cohn about factorization of higher order derivatives of functions in Hardy spaces. We answer in the affirmative a conjecture stated in the same work, therefore giving a complete characterization of the class of symbols $g$ for which the operator is bounded from the Hardy space $H^p$ to $H^q, \, 0<p,q<\infty.$

math.CV↗

arXiv2024

Optimal Domain of generalized Volterra operators

For g in BMOA, we consider the generalized Volterra operator T_g acting on Hardy spaces H^p. This article aims to study the largest space of analytic functions, which is mapped by T_g into the Hardy space H^p. We call this space the optimal domain of T_g and we describe its structural properties. Motivation for this comes from the work of G. Curbera and W. Ricker who studied the optimal domain of the classical Ces\'aro operator.

math.CV↗

arXiv2023

SFC: Near-Source Congestion Signaling and Flow Control

State-of-the-art congestion control algorithms for data centers alone do not cope well with transient congestion and high traffic bursts. To help with these, we revisit the concept of direct \emph{backward} feedback from switches and propose Back-to-Sender (BTS) signaling to many concurrent incast senders. Combining it with our novel approach to in-network caching, we achieve near-source sub-RTT congestion signaling. Source Flow Control (SFC) combines these two simple signaling mechanisms to instantly pause traffic sources, hence avoiding the head-of-line blocking problem of conventional hop-by-hop flow control. Our prototype system and scale simulations demonstrate that near-source signaling can significantly reduce the message completion time of various workloads in the presence of incast, complementing existing congestion control algorithms. Our results show that SFC can reduce the $99^{th}$-percentile flow completion times by $1.2-6\times$ and the peak switch buffer usage by $2-3\times$ compared to the recent incast solutions.

cs.NI↗

arXiv2021

Backpressure Flow Control

Effective congestion control for data center networks is becoming increasingly challenging with a growing amount of latency sensitive traffic, much fatter links, and extremely bursty traffic. Widely deployed algorithms, such as DCTCP and DCQCN, are still far from optimal in many plausible scenarios, particularly for tail latency. Many operators compensate by running their networks at low average utilization, dramatically increasing costs. In this paper, we argue that we have reached the practical limits of end-to-end congestion control. Instead, we propose, implement, and evaluate a new congestion control architecture called Backpressure Flow Control (BFC). BFC provides per-hop per-flow flow control, but with bounded state, constant-time switch operations, and careful use of buffers. We demonstrate BFC's feasibility by implementing it on Tofino2, a state-of-the-art P4-based programmable hardware switch. In simulation, we show that BFC achieves near optimal throughput and tail latency behavior even under challenging conditions such as high network load and incast cross traffic. Compared to existing end-to-end schemes, BFC achieves 2.3 - 60 X lower tail latency for short flows and 1.6 - 5 X better average completion time for long flows.

cs.NI↗