Invariant local Dirichlet forms on locally compact groups
Invariant measures for semigroups
Invariant measures for stochastic Cauchy problems with asymptotically unstable drift semigroup.
Invariant states for positive operator semigroups
Invariant Subspaces and Spectral Conditions on Operator Semigroups
Inverse Cauchy problem and unbiased estimation
Inverse limits need not exist in the category of compact spaces and Feller kernels: a counterexample
Inverses of generators of nonanalytic semigroups
Suppose A is an injective linear operator on a Banach space that generates a uniformly bounded strongly continuous semigroup . It is shown that generates an -regularized semigroup. Several equivalences for generating a strongly continuous semigroup are given. These are used to generate sufficient conditions on the growth of , on subspaces, for generating a strongly continuous semigroup, and to show that the inverse of -d/dx on the closure of its image in L¹([0,∞)) does not generate a strongly...
Isolated points of some sets of bounded cosine families, bounded semigroups, and bounded groups on a Banach space
We show that if the set of all bounded strongly continuous cosine families on a Banach space X is treated as a metric space under the metric of the uniform convergence associated with the operator norm on the space 𝓛(X) of all bounded linear operators on X, then the isolated points of this set are precisely the scalar cosine families. By definition, a scalar cosine family is a cosine family whose members are all scalar multiples of the identity operator. We also show that if the sets of all bounded...
Isoperimetry between exponential and Gaussian.
Joint subnormality of n-tuples and C₀-semigroups of composition operators on L²-spaces
Joint subnormality of a family of composition operators on L²-space is characterized by means of positive definiteness of appropriate Radon-Nikodym derivatives. Next, simplified positive definiteness conditions guaranteeing joint subnormality of a C₀-semigroup of composition operators are supplied. Finally, the Radon-Nikodym derivatives associated to a jointly subnormal C₀-semigroup of composition operators are shown to be the Laplace transforms of probability measures (modulo a C₀-group of scalars)...
Joint subnormality of n-tuples and C₀-semigroups of composition operators on L²-spaces, II
In the previous paper, we have characterized (joint) subnormality of a C₀-semigroup of composition operators on L²-space by positive definiteness of the Radon-Nikodym derivatives attached to it at each rational point. In the present paper, we show that in the case of C₀-groups of composition operators on L²-space the positive definiteness requirement can be replaced by a kind of consistency condition which seems to be simpler to work with. It turns out that the consistency condition also characterizes...
Jump processes, ℒ-harmonic functions, continuity estimates and the Feller property
Given a family of Lévy measures ν={ν(x, ⋅)}x∈ℝd, the present work deals with the regularity of harmonic functions and the Feller property of corresponding jump processes. The main aim is to establish continuity estimates for harmonic functions under weak assumptions on the family ν. Different from previous contributions the method covers cases where lower bounds on the probability of hitting small sets degenerate.
Kantorovich-Rubinstein Maximum Principle in the Stability Theory of Markov Semigroups
A new sufficient condition for the asymptotic stability of a locally Lipschitzian Markov semigroup acting on the space of signed measures is proved. This criterion is applied to the semigroup of Markov operators generated by a Poisson driven stochastic differential equation.
Kato-Protter type inequalities, bounded vectors and the exponential function
Kato's equality and spectral decomposititon for positive C0-Groups.
KMS-symmetric Markov semigroups.
Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space II
This work is concerned with the existence and regularity of solutions to the Neumann problem associated with a Ornstein–Uhlenbeck operator on a bounded and smooth convex set K of a Hilbert space H. This problem is related to the reflection problem associated with a stochastic differential equation in K.
Kolmogorov kernel estimates for the Ornstein-Uhlenbeck operator
Replacing the gaussian semigroup in the heat kernel estimates by the Ornstein-Uhlenbeck semigroup on , we define the notion of Kolmogorov kernel estimates. This allows us to show that under Dirichlet boundary conditions Ornstein-Uhlenbeck operators are generators of consistent, positive, (quasi-) contractive -semigroups on for all and for every domain . For exterior domains with sufficiently smooth boundary a result on the location of the spectrum of these operators is also given.
-analyticity of Schrödinger semigroups on Riemannian manifolds