Wer die Wahrheit des Welzusammenhanges Gottes und der Welt mit eigener Wahrhaftigkeit sucht, wird immer verzweifein, aber gerade in dr Verzweiflung liegt der Beruf.

Not Availabl

The Weiss conjecture on admissibility of observation operators for contraction semigroups

We prove the conjecture of George Weiss for contraction semigroups on Hilbert spaces, giving a characterization of infinite-time admissible observation functionals for a contraction semigroup, namely that such a functional C is infinite-time admissible if and only if there is an M > 0 such that parallel to IC(sI - A)(-1)parallel to less than or equal to M/root Re s for all s in the open right half-plane. Here A denotes the infinitesimal generator of the semigroup. The result provides a simultaneous generalization of several celebrated results from the theory of Hardy spaces involving Carleson measures and Hankel operators

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

Invariant subspaces of the Cesaro operator

This paper explores various classes of invariant subspaces of the classical Ces\`{a}ro operator $C$ on the Hardy space $H^2$. We provide a new characterization of the finite co-dimensional $C$-invariant subspaces, based on earlier work of the first two authors, and determine exactly which model spaces are $C$-invariant subspaces. We also describe the $C$-invariant subspaces contained in model spaces and establish that they are all cyclic. Along the way, we re-examine an associated Hilbert space of analytic functions on the unit disk developed by Kriete and Trutt. We also make a connection between the adjoint of the Ces\`{a}ro operator and certain composition operators on $H^2$ which have universal translates in the sense of Rota.Comment: 36 page

It's not the model, it's the way you use it: exploratory early health economics amid complexity; comment on "problems and promises of health technologies: the role of early health economic modelling"

In a review recently published in this journal, Grutters et al outline the scope and impact of their early health economic modelling of healthcare innovations. Their reflections shed light on ways that health economists can shift-away from traditional reimbursement decision-support, towards a broader role of facilitating the exploration of existing care pathways, and the design of options to implement or discontinue healthcare services. This is a crucial role in organisations that face constant pressure to react and adapt with changes to their existing service configurations, but where there may exist significant disagreement and uncertainty on the extent to which change is warranted. Such dynamics are known to create complex implementation environments, where changes risk being poorly implemented or fail to be sustained. In this commentary, we extend the discussion by Grutters et al on early health economic modelling, to the evaluation of complex interventions and systems. We highlight how early health economic modelling can contribute to a participatory approach for ongoing learning and development within healthcare organisations.Andrew Partington, Jonathan Karno

Mortality among patients with polymyalgia rheumatica: A retrospective cohort study.

OBJECTIVE: To determine whether a diagnosis of polymyalgia rheumatica (PMR) is associated with premature mortality. METHODS: We extracted anonymised electronic medical records of patients over the age of 40 years, who were eligible for linkage with the Office for National Statistics (ONS) Death Registration dataset, from the Clinical Practice Research Datalink from 1990-2016. Patients with PMR were individually matched by age, sex and registered General Practice with up to 5 controls without PMR. The total number and proportion of deaths and mortality rates were calculated. The mortality rate ratio (MRR), with 95% confidence interval (CI), adjusted for age, sex, region, smoking status, body mass index (BMI), and alcohol consumption, was calculated using Poisson regression. The twenty most common causes of death were tabulated. RESULTS: 18,943 patients with PMR were matched to 87,801 controls. Mean (standard deviation) follow-up after date of diagnosis was 8.0 (4.4) years in patients with PMR, and 7.9 (4.6) in controls. PMR was not associated with an increase in the risk of death (adjusted MRR 1.00 [95% CI 0.97, 1.03]) compared to matched controls. Causes of death were broadly similar between patients with PMR and controls, although patients with PMR were slightly more likely to have a vascular cause of death recorded (24% vs 23%). CONCLUSIONS: A diagnosis with PMR does not appear to increase the risk of premature death. Minor variations in cause of death were observed, but overall this study is reassuring for patients with PMR and clinicians