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Petr Kosenko

Publications and source records attributed to Petr Kosenko.

8 recordsLinked to original sources
arXiv2025

On a complex-analytic approach to stationary measures on $S^1$ with respect to the action of $PSU(1,1)$

We provide a complex-analytic approach to the classification of stationary probability measures on $S^1$ with respect to the action of $PSU(1,1)$ on the unit circle via Möbius transformations by studying their Cauchy transforms from the perspective of generalized analytic continuation. We improve upon results of Bourgain and present a complete characterization of Furstenberg measures for Fuchsian groups of first kind via the Brown-Shields-Zeller theorem.

math.DS↗
arXiv2023

Asymptotics of the first-passage function on free and Fuchsian groups

In this preprint we derive explicit estimates for the asymptotics of the first-passage function for a specific class of random walks on free groups and use them to prove the singularity of the hitting measure for a similarly defined class of random walks on Fuchsian groups.

math.PR↗
arXiv2021

The fundamental inequality for cocompact Fuchsian groups

We prove that the hitting measure is singular with respect to Lebesgue measure for any random walk on a cocompact Fuchsian group generated by translations joining opposite sides of a symmetric hyperbolic polygon. Moreover, the Hausdorff dimension of the hitting measure is strictly less than 1. A similar statement is proven for Coxeter groups. Along the way, we prove for cocompact Fuchsian groups a purely geometric inequality for geodesic lengths, strongly reminiscent of the Anderson-Canary-Culler-Shalen inequality for free Kleinian groups.

math.DS↗
arXiv2019

Homological dimensions of smooth crossed products

In this paper we provide upper estimates for the global projective dimensions of smooth crossed products $\mathscr{S}(G, A; α)$ for $G = \mathbb{R}$ and $G = \mathbb{T}$ and a self-induced Fréchet-Arens-Michael algebra $A$. In order to do this, we provide a powerful generalization of methods which are used in the works of Ogneva and Helemskii.

math.FA↗
arXiv2019

Homological dimensions of analytic Ore extensions

If $A$ is an algebra with finite right global dimension, then for any automorphism $α$ and $α$-derivation $δ$ the right global dimension of $A[t; α, δ]$ satisfies \[ \text{rgld} \, A \le \text{rgld} \, A[t; α, δ] \le \text{rgld} \, A + 1. \] We extend this result to the case of holomorphic Ore extensions and smooth crossed products by $\mathbb{Z}$ of $\hat{\otimes}$-algebras.

math.FA↗
arXiv2019

The Arens-Michael envelopes of Laurent Ore extensions

For an Arens-Michael algebra $A$ we consider a class of $A$-$\hat{\otimes}$-bimodules which are invertible with respect to the projective bimodule tensor product. We call such bimodules topologically invertible over $A$. Given a Fréchet-Arens-Michael algebra $A$ and an topologically invertible Fréchet $A$-$\hat{\otimes}$-bimodule $M$, we construct an Arens-Michael algebra $\widehat{L}_A(M)$ which serves as a topological version of the Laurent tensor algebra $L_A(M)$. Also, for a fixed algebra $B$ we provide a condition on an invertible $B$-bimodule $N$ sufficient for the Arens-Michael envelope of $L_B(N)$ to be isomorphic to $\widehat{L}_{\widehat{B}}(\widehat{N})$. In particular, we prove that the Arens-Michael envelope of an invertible Ore extension $A[x, x^{-1}; α]$ is isomorphic to $\widehat{L}_{\widehat{A}}(\widehat{A}_{\widehatα})$ provided that the Arens-Michael envelope of $A$ is metrizable.

math.FA↗
arXiv2019

Orthorecursive expansion of unity

We study the properties of a sequence cn defined by the recursive relation \[\frac{c_0}{n + 1}+\frac{c_1}{n + 2}+\ldots+\frac{c_n}{2n + 1}=0\] for $n>1$ and $c_0=1$. This sequence also has an alternative definition in terms of certain norm minimization in the space $L^2([0, 1])$. We prove estimates on growth order of $c_n$ and the sequence of its partial sums, infinite series identities, connecting $c_n$ with harmonic numbers $H_n$ and also formulate some conjectures based on numerical computations.

math.NT↗