Majorization, 4G Theorem and Schrödinger perturbations
| Autor: | Krzysztof Bogdan, Karol Szczypkowski, Yana A. Butko |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
47D06
47D08 35A08 35B25 Class (set theory) Subordinator 010102 general mathematics Order (ring theory) 01 natural sciences Connection (mathematics) Mathematics - Functional Analysis 010101 applied mathematics Inverse Gaussian distribution symbols.namesake Mathematics (miscellaneous) symbols Fundamental solution 0101 mathematics Majorization Mathematics - Probability Schrödinger's cat Mathematics Mathematical physics |
| Zdroj: | Journal of Evolution Equations. 16:241-260 |
| ISSN: | 1424-3202 1424-3199 |
| Popis: | Schr\"odinger perturbations of transition densities by singular potentials may fail to be comparable with the original transition density. For instance this is so for the transition density of a subordinator perturbed by any time-independent unbounded potential. In order to estimate such perturbations it is convenient to use an auxilary transition density as a majorant and the 4G inequality for the original transition density and the majorant. We prove the 4G inequality for the $1/2$-stable and inverse Gaussian subordinators, discuss the corresponding class of admissible potentials and indicate estimates for the resulting transition densities of Schr\"odinger operators. The connection of the transition densities to their generators is made via the weak-type notion of fundamental solution. Comment: 17 pages, editorial changes and some details added in proofs, to appear in Journal of Evolution Equations |
| Databáze: | OpenAIRE |
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