A non-spectral representation of shift semigroups.
A note on a formula for the fractional powers of infinitesimal generators of semigroups
If -A is the generator of an equibounded -semigroup and 0 < Re α < m (m integer), its fractional power can be described in terms of the semigroup, through a formula that is only valid if a certain function is nonzero. This paper is devoted to the study of the zeros of .
A note on almost periodic solutions of semilinear equations in Banach spaces.
A note on convergence of semigroups
Convergence of semigroups which do not converge in the Trotter-Kato-Neveu sense is considered.
A note on maximal estimates for stochastic convolutions
In stochastic partial differential equations it is important to have pathwise regularity properties of stochastic convolutions. In this note we present a new sufficient condition for the pathwise continuity of stochastic convolutions in Banach spaces.
A note on stability properties of integrated semigroups
A note on the abstract Cauchy problem.
A note on the growth bound of Co-semigroups.
A note on the parabolic differential and difference equations.
A note on the spectral operators of scalar type and semigroups of bounded linear operators.
A Pettis-type integral and applications to transition semigroups
Motivated by applications to transition semigroups, we introduce the notion of a norming dual pair and study a Pettis-type integral on such pairs. In particular, we establish a sufficient condition for integrability. We also introduce and study a class of semigroups on such dual pairs which are an abstract version of transition semigroups. Using our results, we give conditions ensuring that a semigroup consisting of kernel operators has a Laplace transform which also consists of kernel operators....
A probabilistic variant of Chernoff's product formula.
A quantitative asymptotic theorem for contraction semigroups with countable unitary spectrum
Let T be a semigroup of linear contractions on a Banach space X, and let . Then is the annihilator of the bounded trajectories of T*. If the unitary spectrum of T is countable, then is the annihilator of the unitary eigenvectors of T*, and for each x in X.
A refinement of the Poincaré inequality for Kolmogorov operators on .
A remark on parabolic equations.
A semigroup approach to the system with primary and secondary failures.
A sharp result on the exponential operator-norm decay of a family of strongly continuous semigroups.
A spectral mapping theorem for perturbed strongly continuous semigroups.
A spectral mapping theorem for semigroups solving PDEs with nonautonomous past.
A study of boundary value problem for an elliptic equation in Hölder spaces.