On an abstract evolution equation with a spectral operator of scalar type.
On an integral transform by R. S. Phillips
The properties of a transformation by R.S. Phillips, which transforms an exponentially bounded C 0-semigroup of operators T(t) to a Yosida approximation depending on h, are studied. The set of exponentially bounded, continuous functions f: [0, ∞[→ E with values in a sequentially complete L c-embedded space E is closed under the transformation. It is shown that for certain complex h and k, and that , where the limit is uniform in t on compact subsets of the positive real line. If f is Hölder-continuous...
On analytic semigroups and cosine functions in Banach spaces
If A generates a bounded cosine function on a Banach space X then the negative square root B of A generates a holomorphic semigroup, and this semigroup is the conjugate potential transform of the cosine function. This connection is studied in detail, and it is used for a characterization of cosine function generators in terms of growth conditions on the semigroup generated by B. The characterization relies on new results on the inversion of the vector-valued conjugate potential transform.
On -bounded semigroups as a generalization of -semigroups.
On coerciveness in Besov spaces for abstract parabolic equations of higher order
We are concerned with a relation between parabolicity and coerciveness in Besov spaces for a higher order linear evolution equation in a Banach space. As proved in a preceding work, a higher order linear evolution equation enjoys coerciveness in Besov spaces under a certain parabolicity condition adopted and studied by several authors. We show that for a higher order linear evolution equation coerciveness in Besov spaces forces the parabolicity of the equation. We thus conclude that parabolicity...
On differences of heat semigroups
On differences of self-adjoint semigroups
On ergodicity for operators with bounded resolvent in Banach spaces
We prove results on ergodicity, i.e. on the property that the space is a direct sum of the kernel of an operator and the closure of its range, for closed linear operators A such that is uniformly bounded for all α > 0. We consider operators on Banach spaces which have the property that the space is complemented in its second dual space by a projection P. Results on ergodicity are obtained under a norm condition ||I - 2P|| ||I - Q|| < 2 where Q is a projection depending on the operator A....
On exponential dichotomy of semigroups.
On generalized canonical commutation relations
On generators of integrated C-semigroups and C -cosine functions.
On inequalities of Hardy-Sobolev type.
On Liu's analyticity criterion for semigroups.
On nonautonomous second-order differential equations on Banach space.
On optimal regularity in evolution equations
Using interpolation techniques we prove an optimal regularity theorem for the convolution , where is a strongly continuous semigroup in general Banach space. In the case of abstract parabolic problems – that is, when is an analytic semigroup – it lets us recover in a unified way previous regularity results. It may be applied also to some non analytic semigroups, such as the realization of the Ornstein-Uhlenbeck semigroup in , , in which case it yields new optimal regularity results in fractional...
On perturbations of differentiate semigroups.
On reaction-diffusion systems.
On regularity at t = 0 for semilinear ADEs and its numerical applications.
On regularized quasi-semigroups and evolution equations.
On some application of the Bochenek theorem.