| HOME TEACHING (DLA STUDENTÓW) RESEARCH CONTACT |
RESEARCH INTERESTS:
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PREPRINTS:
Quasi-ergodicity of compact strong Feller semigroups on L^2 preprint 2023 Density of states for the Anderson model on nested fractals preprint 2023 Integral kernels of Schrödinger semigroups with nonnegative locally bounded potentials preprint 2023 Relativistic stable operators with critical potentials preprint 2022 |
PUBLICATIONS:
Exponential densities and compound Poisson measures Mathematische Nachrichten 296 (11), 2023, 5077-5108 Bound states and heat kernels for fractional-type Schrödinger operators with singular potentials Communications in Mathematical Physics 403, 2023, 795-828 Heat kernels of non-local Schrödinger operators with Kato potentials Journal of Differential Equations 340, 2022, 273-308 Decay of harmonic functions for discrete time Feynman--Kac operators with confining potentials ALEA, Latin American Journal of Probability and Mathematical Statistics 19, 2022, 1071–1101 On directional convolution equivalent densities Electronic Journal of Probability 27, 2022, no. 65 Lifschitz tail for continuous Anderson models driven by Lévy operators Communications in Contemporary Mathematics 23 (6), 2021, 2050065. Progressive intrinsic ultracontractivity and heat kernel estimates for non-local Schrödinger operators Journal of Functional Analysis 279 (6), 2020, 108606. Lifschitz tail for alloy-type models driven by the fractional Laplacian Journal of Functional Analysis 279 (5), 2020, 108575. Zero-energy bound state decay for nonlocal Schrödinger operators Communications in Mathematical Physics 374, 2020, 2151–2191. Typical long time behaviour of ground state-transformed jump processes Communications in Contemporary Mathematics 22 (2), 2020, 1950002. Reflected Brownian motion on simple nested fractals Fractals: Complex Geometry, Patterns, and Scaling in Nature and Society 27 (6), 2019, 1950104. The quenched asymptotics for nonlocal Schrödinger operators with Poissonian potentials Potential Analysis 52, 2020, 161-202. Spatial asymptotics at infinity for heat kernels of pseudo-differential operators Transactions of the American Mathematical Society 371, 2019, 6627-6663. Lifschitz singularity for subordinate Brownian motions in presence of the Poissonian potential on the Sierpiński gasket Stochastic Processes and their Applications 128 (11), 2018, 3897-3939. Contractivity and ground state domination properties for non-local Schrödinger operators Journal of Spectral Theory 8 (1), 2018, 165-189. Small time sharp bounds for kernels of convolution semigroups Journal d'Analyse Mathématique 132 (1), 2017, 355-394 Fall-off of eigenfunctions for nonlocal Schrödinger operators with decaying potentials Potential Analysis 46 (4), 2017, 647-688 Asymptotic estimate of eigenvalues of pseudo-differential operators in an interval Journal of Mathematical Analysis and Applications 439 (2), 2016, 896-924 Transition in the decay rates of stationary distributions of Lévy motion in an energy landscape Physical Review E 93, 2016, 022135 Estimates of transition densities and their derivatives for jump Lévy processes Journal of Mathematical Analysis and Applications 431 (1), 2015, 260-282 Pointwise eigenfunction estimates and intrinsic ultracontractivity-type properties of Feynman-Kac semigroups for a class of Levy processes Annals of Probability 43 (3), 2015, 1350-1398 Integrated density of states for Poisson-Schrödinger perturbations of subordinate Brownian motions on the Sierpiński gasket Stochastic Processes and their Applications 125 (4), 2015, 1244-1281 Spectral and Analytic Properties of Non-local Schrödinger Operators and Related Jump Processes Communications in Applied and Industrial Mathematics 6 (2), 2014, 534 One-dimensional quasi-relativistic particle in the box Reviews in Mathematical Physics 25 (8), 2013, 1350014 Upper estimates of transition densities for stable dominated semigroups Journal of Evolution Equations 13 (3), 2013, 633-650 Fractional P(\phi)_1 - processes and Gibbs measures Stochastic Processes and their Applications 122 (10), 2012, 3580-3617 Spectral gap lower bound for the one-dimensional fractional Schrödinger operator in the interval Studia Mathematica 209, 2012, 267-287 Intrinsic ultracontractivity for Schrödinger operators based on fractional Laplacians Potential Analysis 33 (4), 2010, 313-339 Boundary Harnack Inequality for α-harmonic functions on the Sierpiński triangle Probability and Mathematical Statistics 30 (2), 2010, 353-368 |
THESES:
Feynman-Kac semigroups of Lévy processes with direct jump property Wrocław University of Science and Technology, 2019 Potential theory of fractional powers of Laplace operator and related Schrödinger operators Wrocław University of Technology, 2011, Supervisor: Prof. T. Kulczycki Potential theory of α-stable motion on fractals (in polish) Wrocław University of Technology, 2008, Supervisors: Prof. T. Byczkowski and Prof. M. Kwaśnicki |
RESEARCH PROJECTS (GRANTS):
Levy processes and non-local Schrödinger operators Principal investigator: K. Kaleta Inequalities and differential equations related to Markov operators Principal investigator: T. Jakubowski Properties of solutions to nonlocal equations Principal investigator: T. Kulczycki Jump Markov processes and their Schrödinger perturbations Principal investigator: K. Kaleta Spectral theory for Levy processes Principal investigator: M. Kwaśnicki Potential theory for fractional powers of Laplacian and related Schrödinger operators Principal investigator: T. Kulczycki Potential theory of a class of Levy processes and their Feynman-Kac semigroups Principal investigator: T. Byczkowski |
CONFERENCES:
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