673,277 research outputs found
Continuity properties of integral kernels associated with Schroedinger operators on manifolds
For Schroedinger operators (including those with magnetic fields) with
singular (locally integrable) scalar potentials on manifolds of bounded
geometry, we study continuity properties of some related integral kernels: the
heat kernel, the Green function, and also kernels of some other functions of
the operator. In particular, we show the joint continuity of the heat kernel
and the continuity of the Green function outside the diagonal. The proof makes
intensive use of the Lippmann-Schwinger equation.Comment: 38 pages, major revision; to appear in Annales Henri Poincare (2007
On the Continuity of Some Functions
We prove that basic arithmetic operations preserve continuity of functions.Institute of Informatics, University of BiaĆystok, Sosnowa 64, 15-887 BiaĆystok, PolandGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Grzegorz Bancerek and Andrzej Trybulec. Miscellaneous facts about functions. Formalized Mathematics, 5(4):485-492, 1996.CzesĆaw ByliĆski. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.CzesĆaw ByliĆski. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.CzesĆaw ByliĆski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.CzesĆaw ByliĆski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.CzesĆaw ByliĆski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.CzesĆaw ByliĆski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.CzesĆaw ByliĆski. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.Agata DarmochwaĆ. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.Agata DarmochwaĆ and Yatsuka Nakamura. Metric spaces as topological spaces - fundamental concepts. Formalized Mathematics, 2(4):605-608, 1991.Artur KorniĆowicz. Arithmetic operations on functions from sets into functional sets. Formalized Mathematics, 17(1):43-60, 2009, doi:10.2478/v10037-009-0005-y.Artur KorniĆowicz and Yasunari Shidama. Intersections of intervals and balls in En/T. Formalized Mathematics, 12(3):301-306, 2004.Artur KorniĆowicz and Yasunari Shidama. Some properties of circles on the plane. Formalized Mathematics, 13(1):117-124, 2005.Beata Padlewska and Agata DarmochwaĆ. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.Andrzej Trybulec. A Borsuk theorem on homotopy types. Formalized Mathematics, 2(4):535-545, 1991.Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003.Andrzej Trybulec and CzesĆaw ByliĆski. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990
On the coarsest topology preserving continuity
We study a topology on a space of functions, called sticking topology, with
the property to be the weakest among the topologies preserving continuity. In
suitable frameworks, this topology preserves borelianity, local integrability,
right continuity and other properties. It is coarser than the locally uniform
convergence and it allows the presence of gliding humps as we show on examples.
We prove relative compactness criteria for this topology and we consider some
extensions.Comment: 14
Refined Solutions of Time Inhomogeneous Optimal Stopping Games via Dirichlet Form
The properties of value functions of time inhomogeneous optimal stopping
problem and zero-sum game (Dynkin game) are studied through time dependent
Dirichlet form. Under the absolute continuity condition on the transition
function of the underlying diffusion process and some other assumptions, the
refined solutions without exceptional starting points are proved to exist, and
the value functions of the optimal stopping and zero-sum game, which are finely
and cofinely continuous, are characterized as the solutions of some variational
inequalities, respectively
Barrier functions for Pucci-Heisenberg operators and applications
The aim of this article is the explicit construction of some barrier
functions ("fundamental solutions") for the Pucci-Heisenberg operators. Using
these functions we obtain the continuity property, up to the boundary, for the
viscosity solution of fully non-linear Dirichlet problems on the Heisenberg
group, if the boundary of the domain satisfies some regularity geometrical
assumptions (e.g. an exterior Heisenberg-ball condition at the characteristic
points). We point out that the knowledge of the fundamental solutions allows
also to obtain qualitative properties of Hadamard, Liouville and Harnack type
- âŠ