Zobrazeno 1 - 10
of 204
pro vyhledávání: '"Bogdan, Krzysztof"'
We construct a strong Markov process corresponding to the Dirichlet form of Servadei and Valdinoci and use the process to solve the corresponding Neumann boundary problem for the fractional Laplacian and the half-line.
Comment: 85 pages
Comment: 85 pages
Externí odkaz:
http://arxiv.org/abs/2411.08220
Autor:
Bogdan, Krzysztof, Kunze, Markus
We construct a Hunt process that can be described as an isotropic $\alpha$-stable L\'evy process reflected from the complement of a bounded open Lipschitz set. In fact, we introduce a new analytic method for concatenating Markov processes. It is base
Externí odkaz:
http://arxiv.org/abs/2410.03516
Motivated by the spectral theory of relativistic atoms, we prove matching upper and lower bounds for the transition density of Hardy perturbations of subordinated Bessel heat kernels. The analysis is based on suitable supermedian functions, in partic
Externí odkaz:
http://arxiv.org/abs/2409.02853
We give Martin representation of nonnegative functions caloric with respect to the fractional Laplacian in Lipschitz open sets. The caloric functions are defined in terms of the mean value property for the space-time isotropic $\alpha$-stable L\'evy
Externí odkaz:
http://arxiv.org/abs/2403.03840
We prove the Hardy--Stein identity for vector functions in $L^p(\mathbb R^d;\mathbb R^n)$ with $1
Externí odkaz:
http://arxiv.org/abs/2309.09856
Autor:
Bogdan, Krzysztof, Merz, Konstantin
We prove new bounds for Bessel heat kernels and Bessel heat kernels subordinated by stable subordinators. In particular, we provide a 3G inequality in the subordinated case.
Comment: 18 pages
Comment: 18 pages
Externí odkaz:
http://arxiv.org/abs/2308.15026
We construct a self-similar solution of the heat equation for the fractional Laplacian with Dirichlet boundary conditions in every fat cone. As applications, we give the Yaglom limit and entrance law for the corresponding killed isotropic stable L\'{
Externí odkaz:
http://arxiv.org/abs/2307.01825
Autor:
Bogdan, Krzysztof, Merz, Konstantin
Publikováno v:
J. Math. Pures Appl. (9) 186 (2024), 176-204
Motivated by the study of relativistic atoms, we consider the Hardy operator $(-\Delta)^{\alpha/2}-\kappa|x|^{-\alpha}$ acting on functions of the form $u(|x|) |x|^{\ell} Y_{\ell,m}(x/|x|)$ in $L^2(\mathbb{R}^d)$, when $\kappa\geq0$ and $\alpha\in(0,
Externí odkaz:
http://arxiv.org/abs/2305.00881
Autor:
Bogdan, Krzysztof, Jastrzȩbski, Kajetan, Kassmann, Moritz, Kijaczko, Michał, Popławski, Paweł
The shot-down process is a strong Markov process which is annihilated, or shot down, when jumping over or to the complement of a given open subset of a vector space. Due to specific features of the shot-down time, such processes suggest new type of b
Externí odkaz:
http://arxiv.org/abs/2301.12290
Autor:
Hansen, Wolfhard, Bogdan, Krzysztof
For open sets $U$ in some space $X$, we are interested in positive solutions to semi-linear equations $ Lu=\varphi(\cdot,u)\mu$ on $U$. Here $L$ may be an elliptic or parabolic operator of second order (generator of a diffusion process) or an integro
Externí odkaz:
http://arxiv.org/abs/2212.13999