Criteria for ultracontractivity
C-semigroups on Banach spaces and functional inequalities
Decoherence of quantum Markov semigroups
Decomposable embeddings, complete trajectories, and invariant subspaces
We produce closed nontrivial invariant subspaces for closed (possibly unbounded) linear operators, A, on a Banach space, that may be embedded between decomposable operators on spaces with weaker and stronger topologies. We show that this can be done under many conditions on orbits, including when both A and A* have nontrivial non-quasi-analytic complete trajectories, and when both A and A* generate bounded semigroups that are not stable.
Decomposing and twisting bisectorial operators
Bisectorial operators play an important role since exactly these operators lead to a well-posed equation u'(t) = Au(t) on the entire line. The simplest example of a bisectorial operator A is obtained by taking the direct sum of an invertible generator of a bounded holomorphic semigroup and the negative of such an operator. Our main result shows that each bisectorial operator A is of this form, if we allow a more general notion of direct sum defined by an unbounded closed projection. As a consequence...
Decomposition and disintegration of positive definite kernels on convex *-semigroups
The paper deals with operator-valued positive definite kernels on a convex *-semigroup whose Kolmogorov-Aronszajn type factorizations induce *-semigroups of bounded shift operators. Any such kernel Φ has a canonical decomposition into a degenerate and a nondegenerate part. In case is commutative, Φ can be disintegrated with respect to some tight positive operator-valued measure defined on the characters of if and only if Φ is nondegenerate. It is proved that a representing measure of a positive...
Decompositions of Beurling type for E₀-semigroups
We define tensor product decompositions of E₀-semigroups with a structure analogous to a classical theorem of Beurling. Such decompositions can be characterized by adaptedness and exactness of unitary cocycles. For CCR-flows we show that such cocycles are convergent.
Decompositions of operator-valued functions in Hilbert spaces
Decompositions of tensor products of contractions
Degenerate convergence of semigroups.
Density theorems for measurable transformations
Dependence of a weak solution of the first order differential equation on a parameter.
Dependence results on almost periodic and almost automorphic solutions of evolution equations.
Der Generator stark stetiger Verbandshalbgruppen auf C (X) und dessen Spektrum.
Desch-Schappacher perturbation theorem for -semigroups on the dual of a Banach space.
Diagonalisation d'opérateurs non-autoadjoints et séparation des variables
Dichotomy and functional calculi.
Die erzeugte Algebra eines Markov-Verbandsoperators in C(X).
Differentiability of perturbed semigroups and delay semigroups
Suppose that A generates a C₀-semigroup T on a Banach space X. In 1953 R. S. Phillips showed that, for each bounded operator B on X, the perturbation A+B of A generates a C₀-semigroup on X, and he considered whether certain classes of semigroups are stable under such perturbations. This study was extended in 1968 by A. Pazy who identified a condition on the resolvent of A which is sufficient for the perturbed semigroups to be immediately differentiable. However, M. Renardy showed in 1995 that immediate...
Differential operators with non dense domain