Liouville's theorems for L\'evy operators
T Grzywny, M Kwaśnicki - arXiv preprint arXiv:2301.08540, 2023 - arxiv.org
Let $ L $ be a L\'evy operator. A function $ h $ is said to be harmonic with respect to $ L $ if $
L h= 0$ in an appropriate sense. We prove Liouville's theorem for positive functions …
L h= 0$ in an appropriate sense. We prove Liouville's theorem for positive functions …
[HTML][HTML] Bound states and heat kernels for fractional-type Schrödinger operators with singular potentials
T Jakubowski, K Kaleta, K Szczypkowski - … in Mathematical Physics, 2023 - Springer
We consider non-local Schrödinger operators H=-LV in L 2 (R d), d⩾ 1, where the kinetic
terms L are pseudo-differential operators which are perturbations of the fractional Laplacian …
terms L are pseudo-differential operators which are perturbations of the fractional Laplacian …
[PDF][PDF] Relativistic stable operators with critical potentials
T Jakubowski, K Kaleta, K Szczypkowski - arXiv preprint arXiv:2208.00687, 2022 - arxiv.org
arXiv:2208.00687v2 [math.AP] 21 Mar 2023 Page 1 RELATIVISTIC STABLE OPERATORS
WITH CRITICAL POTENTIALS TOMASZ JAKUBOWSKI, KAMIL KALETA, AND KAROL …
WITH CRITICAL POTENTIALS TOMASZ JAKUBOWSKI, KAMIL KALETA, AND KAROL …
Quasi-ergodicity of compact strong Feller semigroups on
K Kaleta, RL Schilling - arXiv preprint arXiv:2304.12834, 2023 - arxiv.org
We study the quasi-ergodicity of compact strong Feller semigroups $ U_t $, $ t> 0$, on $ L^
2 (M,\mu) $; we assume that $ M $ is a locally compact Polish space equipped with a locally …
2 (M,\mu) $; we assume that $ M $ is a locally compact Polish space equipped with a locally …
Integral kernels of Schr\" odinger semigroups with nonnegative locally bounded potentials
M Baraniewicz, K Kaleta - arXiv preprint arXiv:2302.13886, 2023 - arxiv.org
We give the upper and the lower estimates of heat kernels for Schr\" odinger operators $ H=-
\Delta+ V $, with nonnegative and locally bounded potentials $ V $ in $\mathbb {R}^ d …
\Delta+ V $, with nonnegative and locally bounded potentials $ V $ in $\mathbb {R}^ d …
Decay of harmonic functions for discrete time Feynman--Kac operators with confining potentials
We propose and study a certain discrete time counterpart of the classical Feynman--Kac
semigroup with a confining potential in countable infinite spaces. For a class of long range …
semigroup with a confining potential in countable infinite spaces. For a class of long range …
[HTML][HTML] Heat kernels of non-local Schrödinger operators with Kato potentials
We study heat kernels of Schrödinger operators whose kinetic terms are non-local operators
built for sufficiently regular symmetric Lévy measures with radial decreasing profiles and …
built for sufficiently regular symmetric Lévy measures with radial decreasing profiles and …
Lifshitz tail for continuous Anderson models driven by Levy operators
K Kaleta, K Pietruska-Pałuba - Communications in Contemporary …, 2021 - World Scientific
We investigate the behavior near zero of the integrated density of states for random
Schrödinger operators Φ (− Δ)+ V ω in L 2 (ℝ d), d≥ 1, where Φ is a complete Bernstein …
Schrödinger operators Φ (− Δ)+ V ω in L 2 (ℝ d), d≥ 1, where Φ is a complete Bernstein …
Exponential densities and compound Poisson measures
M Baraniewicz, K Kaleta - Mathematische Nachrichten, 2023 - Wiley Online Library
We prove estimates at infinity of convolutions fn★ f^n⋆ and densities of the corresponding
compound Poisson measures for a class of radial decreasing densities on R d R^d, d≥ 1 …
compound Poisson measures for a class of radial decreasing densities on R d R^d, d≥ 1 …
On directional convolution equivalent densities
K Kaleta, D Ponikowski - Electronic Journal of Probability, 2022 - projecteuclid.org
We propose a definition of directional multivariate subexponential and convolution
equivalent densities and find a useful characterization of these notions for a class of …
equivalent densities and find a useful characterization of these notions for a class of …