Notes on analytic convoluted C-semigroups

Convoluted C-cosine Functions and Convoluted C-semigroups

Perturbation Theorems for Convoluted C-semigroups and Cosine Functions

On Analytic Integrated Semigroups

The known definition of an analytic n-times integrated semigroup is reconsidered and one superfluous condition is removed. It is proved that every densely defined generator of an exponentially bounded, analytic n-times integrated semigroup of angle α with the appropriate growth rate at zero is also the generator of an analytic C0-semigroup of the same angle. AMS Mathematics Subject Classificati...

Lecture Notes on SEMIGROUPS

Goes to the advanced topics rather fast. Contains up-to-date proofs for free inverse semigroups, topics on biordered sets, Isbell's zigzags , and some combinatorics of transformation semigroups.] Fundamentals of semigroup theory, 1995. [Probably the best introduction. Contains more advanced material such as Isbell's zigzags , and the free inverse semi-groups]. G. Lallement, Semigroups and combi...

On the Weiss Conjecture for Analytic Semigroups

Let T(t) be an analytic semigroup with generator A on some Banach space. Le Merdy in [12] showed the validity of the so-called Weiss conjecture : C ∈ L(D(A), Y ) is an admissible observation operator if and only if {‖C(λI − A)−1‖ Reλ ≥ α for some α > 0} is a bounded set, is equivalent to the finite-time admissibility of the fractional power (−A)1/2 for A. The proof was essentially based on the ...