4 papers
Sharp and plain estimates for Schrödinger perturbation of Gaussian kernel
Tomasz Jakubowski, Karol Szczypkowski
We investigate whether a fundamental solution of the Schrödinger equation has local in time sharp Gaussian estimates. We compare that class with the class…
L{é}vy processes: concentration function and heat kernel bounds
Tomasz Grzywny, Karol Szczypkowski
We investigate densities of vaguely continuous convolution semigroups of probability measures on . We expose that many typical conditions on the characteristic expone…
Heat kernels of non-symmetric Lévy-type operators
Tomasz Grzywny, Karol Szczypkowski
We construct the fundamental solution (the heat kernel) to the equation , where under certain assumptions the operator takes one of…
Characterization of sharp global Gaussian estimates for Schrödinger heat kernels
Krzysztof Bogdan, Jacek Dziubański, Karol Szczypkowski
We investigate when the fundamental solution of the Schrödinger equation posseses sharp Gaussian bounds global in space and time. We give a characterization for $V…