6 papers
IDS for subordinate Brownian motions in Poisson random environment on nested fractals
Hubert Balsam, Kamil Kaleta, Mariusz Olszewski +1
We establish the Lifshitz singularity of the integrated density of states (IDS) for random Schrödinger operators \[ H^Ï = Ï(-\mathcal{L}) + V^Ï \] on planar unbounded nested fr…
Smoothing on for ground state transformed semigroups in non-local settings
MiÅosz Baraniewicz, Kamil Kaleta
We study the -smoothing properties for a broad class of semigroups arising from the ground state transformation of Schrödinger semigroups with confining potentials associated…
Heat kernels, intrinsic contractivity and ergodicity of discrete-time Markov chains killed by potentials
Wojciech Cygan, Kamil Kaleta, René L. Schilling +1
We study discrete-time Markov chains on countably infinite state spaces, which are perturbed by rather general confining (i.e.\ growing at infinity) potentials. Using a discrete-ti…
Decay of resolvent kernels and Schrödinger eigenstates for Lévy operators
Kamil Kaleta, René L. Schilling, PaweŠSztonyk
We study the spatial decay behaviour of resolvent kernels for a large class of non-local Lévy operators and bound states of the corresponding Schrödinger operators. Our findings…
Heat kernels and Green functions for fractional Schrödinger operators with confining potentials
Xin Chen, Kamil Kaleta, Jian Wang
We give two-sided, global (in all variables) estimates of the heat kernel and the Green function of the fractional Schrödinger operator with a non-negative and locally bounded pot…
Relativistic stable operators with critical potentials
Tomasz Jakubowski, Kamil Kaleta, Karol Szczypkowski
We give local in time sharp two sided estimates of the heat kernel associated with the relativistic stable operator perturbed by a critical (Hardy) potential.