C₀-semigroups of 2-isometries and Dirichlet spaces

In the context of a theorem of Richter, we establish a similarity between C₀-semigroups of analytic 2-isometries {T(t)}t≥0 acting on a Hilbert space H and the multiplication operator semigroup {Mϕt}t≥0 induced by ϕt(s)=exp(−st) for s in the right-half plane C₊ acting boundedly on weighted Dirichlet spaces on C₊. As a consequence, we derive a connection with the right shift semigroup {St}t≥0 given by Stf(x)={0 if 0≤x≤t,f(x−t) if x>t, acting on a weighted Lebesgue space on the half line R+ and address some applications regarding the study of the invariant subspaces\linebreak of C₀-semigroups of analytic 2-isometries

On the Wandering Property in Dirichlet spaces

We show that in a scale of weighted Dirichlet spaces Dα, including the Bergman space, given any finite Blaschke product B there exists an equivalent norm in Dα such that B satisfies the wandering subspace property with respect to such norm. This extends, in some sense, previous results by Carswell et al. (Indiana Univ Math J 51(4):931–961, 2002). As a particular instance, when B(z)=zk and |α|≤log(2)log(k+1), the chosen norm is the usual one in Dα

Weighted composition operators on the Dirichlet space: boundedness and spectral properties

Boundedness of weighted composition operators W u,φ acting on the classical Dirichlet space D as W u,φ f=u(f∘φ) is studied in terms of the multiplier space associated to the symbol φ , i.e., M(φ)={u∈D:W u,φ is bounded on D} . A prominent role is played by the multipliers of the Dirichlet space. As a consequence, the spectrum of W u,φ in D whenever φ is an automorphism of the unit disc is studied, extending a recent work of Hyvärinen et al. (J. Funct. Anal. 265:1749–1777, 2013) to the context of the Dirichlet space

A922 Sequential measurement of 1 hour creatinine clearance (1-CRCL) in critically ill patients at risk of acute kidney injury (AKI)

Meeting abstrac

Norm estimates for weighted composition operators on spaces of holomorphic functions

This paper shows that the boundedness of a weighted composition operator on the Hardy-Hilbert space on the disc or half-plane implies its boundedness on a class of related spaces, including weighted Bergman spaces. The methods used involve the study of lower-triangular and causal operators