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pro vyhledávání: '"Karlsson Anders"'
This paper illustrates the utility of the heat kernel on $\mathbb{Z}$ as the discrete analogue of the Gaussian density function. It is the two-variable function $K_{\mathbb{Z}}(t,x)=e^{-2t}I_{x}(2t)$ involving a Bessel function and variables $x\in\ma
Externí odkaz:
http://arxiv.org/abs/2409.14344
Autor:
Izeki, Hiroyasu, Karlsson, Anders
We show that finitely generated groups which are Liouville and without infinite finite-dimensional linear representations must have a global fixed point whenever they act by isometry on a finite-dimensional complete CAT(0)-space. This provides a part
Externí odkaz:
http://arxiv.org/abs/2404.19273
Let $G$ be an infinite, edge- and vertex-weighted graph with certain reasonable restrictions. We construct the heat kernel of the associated Laplacian using an adaptation of the parametrix approach due to Minakshisundaram-Pleijel in the setting of Ri
Externí odkaz:
http://arxiv.org/abs/2404.11535
This work concerns the design of perfectly conducting objects that are invisible to an incident transverse magnetic plane wave. The object in question is a finite planar waveguide with a finite periodic array of barriers. By optimizing this array, th
Externí odkaz:
http://arxiv.org/abs/2310.06132
In this paper we develop the parametrix approach for constructing the heat kernel on a graph $G$. In particular, we highlight two specific cases. First, we consider the case when $G$ is embedded in a Eulidean domain or manifold $\Omega$, and we use a
Externí odkaz:
http://arxiv.org/abs/2308.04174
Let $X_m$ denote the discrete circle with $m$ vertices. For $x,y\in X_{m}$ and complex $s$, let $G_{X_m,\chi_{\beta}}(x,y;s)$ be the resolvent kernel associated to the combinatorial Laplacian which acts on the space of functions on $X_{m}$ that are t
Externí odkaz:
http://arxiv.org/abs/2305.00202
Autor:
Karlsson, Anders
This text reviews certain notions in metric geometry that may have further applications to problems in complex geometry and holomorphic dynamics in several variables. The discussion contains a few unrecorded results and formulates a number of questio
Externí odkaz:
http://arxiv.org/abs/2302.12671
Autor:
Karlsson, Anders
We discuss certain recent metric space methods and some of the possibilities these methods provide, with special focus on various generalizations of Lyapunov exponents originally appearing in the theory of dynamical systems and differential equations
Externí odkaz:
http://arxiv.org/abs/2212.13097
Publikováno v:
Advances in Mathematics, 2024
We study the interplay between the backward dynamics of a non-expanding self-map $f$ of a proper geodesic Gromov hyperbolic metric space $X$ and the boundary regular fixed points of $f$ in the Gromov boundary. To do so, we introduce the notion of sta
Externí odkaz:
http://arxiv.org/abs/2210.17480
Volumes of spheres and special values of zeta functions of $\mathbb{Z}$ and $\mathbb{Z}/n\mathbb{Z}$
The volume of the unit sphere in every dimension is given a new interpretation as a product of special values of the zeta function of $\mathbb{Z}$, akin to volume formulas of Minkowski and Siegel in the theory of arithmetic groups. A product formula
Externí odkaz:
http://arxiv.org/abs/2209.03590