Time-dependent Schrödinger perturbations of transition densities

Krzysztof Bogdan, Wolfhard Hansen, and Tomasz Jakubowski. "Time-dependent Schrödinger perturbations of transition densities." Studia Mathematica 189.3 (2008): 235-254. <http://eudml.org/doc/285325>.

@article{KrzysztofBogdan2008,
abstract = {We construct the fundamental solution of $∂_t - Δ_y - q(t,y)$ for functions q with a certain integral space-time relative smallness, in particular for those satisfying a relative Kato condition. The resulting transition density is comparable to the Gaussian kernel in finite time, and it is even asymptotically equal to the Gaussian kernel (in small time) under the relative Kato condition. The result is generalized to arbitrary strictly positive and finite time-nonhomogeneous transition densities on measure spaces. We also discuss specific applications to Schrödinger perturbations of the fractional Laplacian in view of the fact that the 3P Theorem holds for the fundamental solution corresponding to the operator.},
author = {Krzysztof Bogdan, Wolfhard Hansen, Tomasz Jakubowski},
journal = {Studia Mathematica},
keywords = {relative Kato condition; conditional process},
language = {eng},
number = {3},
pages = {235-254},
title = {Time-dependent Schrödinger perturbations of transition densities},
url = {http://eudml.org/doc/285325},
volume = {189},
year = {2008},
}

TY - JOUR
AU - Krzysztof Bogdan
AU - Wolfhard Hansen
AU - Tomasz Jakubowski
TI - Time-dependent Schrödinger perturbations of transition densities
JO - Studia Mathematica
PY - 2008
VL - 189
IS - 3
SP - 235
EP - 254
AB - We construct the fundamental solution of $∂_t - Δ_y - q(t,y)$ for functions q with a certain integral space-time relative smallness, in particular for those satisfying a relative Kato condition. The resulting transition density is comparable to the Gaussian kernel in finite time, and it is even asymptotically equal to the Gaussian kernel (in small time) under the relative Kato condition. The result is generalized to arbitrary strictly positive and finite time-nonhomogeneous transition densities on measure spaces. We also discuss specific applications to Schrödinger perturbations of the fractional Laplacian in view of the fact that the 3P Theorem holds for the fundamental solution corresponding to the operator.
LA - eng
KW - relative Kato condition; conditional process
UR - http://eudml.org/doc/285325
ER -