In order to develop a differential calculus for error propagation (cf [3]) we study local Dirichlet forms on probability spaces with carré du champ Γ – i.e. error structures – and we are looking for an object related to Γ which is linear and with a good behaviour by images. For this we introduce a new notion called the measure valued gradient which is a randomized square root of Γ. The expositi...

B. G. Bodmann (2004): A lower bound for the Wehrl entropy of quantum spin with sharp high-spin asymptotics, Commun. Math. Phys. 250, 287300. Uncertainty principles and optimization constitute a central theme in Bodmann’s research related to harmonic analysis and its applications. For many Hilbert spaces equipped with a reproducing kernel, it seems plausible that kernel functions should be most ...

We show that if u is a compactly supported distribution on the complex plane such that, for every pair of entire functions f, g, $$\begin{aligned} \langle u,f{\overline{g}}\rangle =\langle u,f\rangle u,{\overline{g}}\rangle , \end{aligned}$$ then at single point. As an application, we complete classification all weighted Dirichlet spaces unit disk are de Branges–Rovnyak by showing spaces, weigh...

We consider reproducing kernel Hilbert spaces of Dirichlet series with kernels of the form k(s, u) = ∑ ann −s−ū, and characterize when such a space is a complete Pick space. We then discuss what it means for two reproducing kernel Hilbert spaces to be “the same”, and introduce a notion of weak isomorphism. Many of the spaces we consider turn out to be weakly isomorphic as reproducing kernel Hil...