Recently in [17, 18], we extended the concept of intrinsic ultracontractivity to nonsymmetric semigroups and proved that for a large class of non-symmetric diffusions Z with measure-valued drift and potential, the semigroup of ZD (the process obtained by killing Z upon exiting D) in a bounded domain is intrinsic ultracontractive under very mild assumptions. In this paper, we study the intrinsic...

In this work, we show that a strongly continuous semigroup generated by a normal operator N is conjugate to the semigroup generated by the real part of N , provided zero is not an eigenvalue of the real part of N . We also show that in case N satisfies a certain sectorial property, the homeomorphism establishing the conjugacy, as well as its inverse, is locally Hölder continuous. Moreover, in c...

We show that every continuous product system of correspondences over a unital C∗–algebra occurs as the product system of a strictly continuous E0–semigroup.

In this paper we investigate and compare the properties of the semigroup generated by A, and the sequence Ad , n ∈ N, where Ad = (I +A)(I −A)−1. We show that if A and A−1 generate a uniformly bounded, strongly continuous semigroup on a Hilbert space, then Ad is power bounded. For analytic semigroups we can prove stronger results. If A is the infinitesimal generator of an analytic semigroup, the...

A topological semigroup is a nonvoid, Hausdorff space, 5, together with a continuous, associative multiplication defined on 5. Here the term semigroup will always denote a topological semigroup. In [4], Wallace and Koch have shown that if the circle, B, is a semigroup such that B2 = B, then either B is a group, or the multiplication on B is of the trivial kind xy = x, or xy = y. In [6], Mostert...

Let A be a simple, separable C∗-algebra of stable rank one. We prove that the Cuntz semigroup of C(T, A) is determined by its Murray-von Neumann semigroup of projections and a certain semigroup of lower semicontinuous functions (with values in the Cuntz semigroup of A). This result has two consequences. First, specializing to the case that A is simple, finite, separable and Z-stable, this yield...

Subshifts are sets of configurations over an infinite grid defined by a set of forbidden patterns. In this thesis, we study two-dimensional subshifts of finite type (2D SFTs), where the underlying grid is Z and the set of forbidden patterns is finite. We are mainly interested in the interplay between the computational power of 2D SFTs and their geometry, examined through the concept of expansiv...

This paper studies the notions of controllability for the linear systems associated with the generator of an exponentially bounded C-semigroup in a Banach space, controls also belonging to Banach spaces. Necessary and sufficient conditions are obtained in that framework, and the duality property is studied, which generalize the corresponding results of the linear systems associated with the gen...

We consider continuous semigroups of analytic functions {Φt}t≥0 in the so-called Gordon-Hedenmalm class G, that is, family Φ:C+→C+ giving rise to bounded composition operators Hardy space Dirichlet series H2. show there is a one-to-one correspondence between G and strongly {Tt}t≥0, where Tt(f)=f∘Φt, f∈H2. extend these results for range p∈[1,∞). For case p=∞, we prove no non-trivial semigroup H∞...