Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 10

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

The boundary Harnack principle for the fractional Laplacian

100%
Bogdan K.
Studia Mathematica
|
1997
|
tom 123
|
nr 1
43-80
EN
We study nonnegative functions which are harmonic on a Lipschitz domain with respect to symmetric stable processes. We prove that if two such functions vanish continuously outside the domain near a part of its boundary, then their ratio is bounded near this part of the boundary.
2
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Applied Mathematics on joint Meeting of UMI-SIMAI-PTM, September 17-20, 2018

64%
Grzywny T., Bogdan K.
Mathematica Applicanda
|
2018
|
tom 46
|
nr 2
EN
The 2018 Forum of Mathematician was organized with cooperation of Italian Mathematical Union (Union e Matematica Italiana) and the Italian Society of Industrial and Applied Mathematics (Società Italiana di Matematica Applicata e Industriale). The meeting aims at continuation of the tradition of bilateral meetings held in the last years by the Polish Mathematical Society together with other national societies. This forum does not exclude the participation of mathematicians from other countries. The Forum in Wroclaw also hosted a large group of participants from outside Poland and Italy. The meeting was hosted by the Faculty Mathematics and Computer Science of the University of Wrocław and the Faculty of of Pure and Applied Mathematics of Wrocław University of Science and Technology. It was the fourth bilateral symposium of PTM after the Second World War (cf. Duda(2018)): AMS-PTM Joint Meeting (Warsaw) in 2007, IMU-PTM Joint meeting (Łódź) in 2011 and DMV-PTM Joint Metting (Poznań) in 2014.
3
Content available remote

Gaussian estimates for Schrödinger perturbations

64%
Bogdan K., Szczypkowski K.
Studia Mathematica
|
2014
|
tom 221
|
nr 2
151-173
EN
We propose a new general method of estimating Schrödinger perturbations of transition densities using an auxiliary transition density as a majorant of the perturbation series. We present applications to Gaussian bounds by proving an optimal inequality involving four Gaussian kernels, which we call the 4G Theorem. The applications come with honest control of constants in estimates of Schrödinger perturbations of Gaussian-type heat kernels and also allow for specific non-Kato perturbations.
4
Content available remote

Heat kernel of fractional Laplacian in cones

64%
Bogdan K., Grzywny T.
Colloquium Mathematicum
|
2010
|
tom 118
|
nr 2
365-377
EN
We give sharp estimates for the transition density of the isotropic stable Lévy process killed when leaving a right circular cone.
5
Content available remote

Relative Fatou theorem for harmonic functions of rotation invariant stable processes in smooth domains

64%
Bogdan K., Dyda B.
Studia Mathematica
|
2003
|
tom 157
|
nr 1
83-96
EN
For $C^{1,1}$ domains we give exact asymptotics near the domain's boundary for the Green function and Martin kernel of the rotation invariant α-stable Lévy process. We also obtain a relative Fatou theorem for harmonic functions of the stable process.
6
Content available remote

Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains

64%
Bogdan K., Byczkowski T.
Studia Mathematica
|
1999
|
tom 133
|
nr 1
53-92
EN
The purpose of the paper is to extend results of the potential theory of the classical Schrödinger operator to the α-stable case. To obtain this we analyze a weak version of the Schrödinger operator based on the fractional Laplacian and we prove the Conditional Gauge Theorem.
7
Content available remote

Estimates of the potential kernel and Harnack's inequality for the anisotropic fractional Laplacian

64%
Bogdan K., Sztonyk P.
Studia Mathematica
|
2007
|
tom 181
|
nr 2
101-123
EN
We characterize those homogeneous translation invariant symmetric non-local operators with positive maximum principle whose harmonic functions satisfy Harnack's inequality. We also estimate the corresponding semigroup and the potential kernel.
8
Content available remote

Time-dependent Schrödinger perturbations of transition densities

51%
Bogdan K., Hansen W., Jakubowski T.
Studia Mathematica
|
2008
|
tom 189
|
nr 3
235-254
EN
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.
9
Content available remote

Fourier multipliers for non-symmetric Lévy processes

51%
Bañuelos R., Bielaszewski A., Bogdan K.
Banach Center Publications
|
2011
|
tom 95
|
nr 1
9-25
EN
We study Fourier multipliers resulting from martingale transforms of general Lévy processes.
10
Content available remote

Harnack inequality for stable processes on d-sets

51%
Bogdan K., Stós A., Sztonyk P.
Studia Mathematica
|
2003
|
tom 158
|
nr 2
163-198
EN
We investigate properties of functions which are harmonic with respect to α-stable processes on d-sets such as the Sierpiński gasket or carpet. We prove the Harnack inequality for such functions. For every process we estimate its transition density and harmonic measure of the ball. We prove continuity of the density of the harmonic measure. We also give some results on the decay rate of harmonic functions on regular subsets of the d-set. In the case of the Sierpiński gasket we even obtain the Boundary Harnack Principle.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.