Faculty of Mathematics
Collaborative Research Centre 701
Spectral Structures and Topological Methods in Mathematics
stripes SFB701

Project A8

Fine properties of long-range operators and processes


Principal Investigator(s) Other Investigators
Moritz Kaßmann
Jamil Chaker
Andrea Nickel
Tim Schulze
Karol Szczypkowski
Paul Voigt

Summary:

In this project, we study fine properties of nonlocal operators and their corresponding stochastic processes. The operators under consideration may be regarded as generalizations of powers of the Laplace operator (with exponent less than one) and alpha-stable jump processes to a natural class of integro-differential operators and jump processes. To some extent, one can consider these objects as nonlocal analogs to diffusion operators and diffusions. There has recently been an increasing interest in such non-local operators and corresponding jump processes from various different viewpoints. The project concentrates on fine properties such as pointwise estimates. Both, techniques and problems, are related to analysis, partial differential equations and stochastic processes at the same time.

Recent Preprints:

17003 Discrete versions of the Li-Yau gradient estimate PDF | PS.GZ
16020 Characterization of sharp global Gaussian estimates for Schrödinger heat kernels PDF | PS.GZ
16010 Scaling invariant Harnack inequalities in a general setting PDF | PS.GZ
15047 On a question of Liskevich and Semenov PDF | PS.GZ
15045 Intrinsic Hoelder continuity of harmonic functions PDF | PS.GZ
15017 Kato classes for Lévy processes PDF | PS.GZ
14071 Majorization, 4G theorem and Schrödinger perturbations PDF | PS.GZ
14059 Harnack inequalities for Hunt processes with Green function PDF | PS.GZ
14019 Unavoidable collections of balls for processes with isotropic unimodal Green function PDF | PS.GZ
13047 Unavoidable sets and harmonic measures living on small sets PDF | PS.GZ