Abstract We characterize all semigroups sandwiched between the semigroup of a Dirichlet form and the semigroup of its active main part. In case the Dirichlet form is regular, we give a more explicit description of the quadratic forms of the sandwiched semigroups in terms of pairs consisting of an open…
We give a sufficient condition for non-existence of global nonnegative mild solutions of the Cauchy problem for the semilinear heat equation u ′ = L u + f ( u ) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}…
The third edition of Flow Cytometry Guidelines provides the key aspects to consider when performing flow cytometry experiments and includes comprehensive sections describing phenotypes and functional assays of all major human and murine immune cell subsets. Notably, the Guidelines contain helpful tables…
Entropy is a well-studied concept and the literature contains a vast amount of material on this concept in the context of actions of countable discrete amenable groups. In this thesis we extend several statements about entropy and topological pressure to the context of unimodular amenable groups. This…
Modulated crystals and quasicrystals can simultaneously be described as modulated quasicrystals, a class of point sets introduced by de Bruijn in 1987. With appropriate modulation functions, modulated quasicrystals themselves constitute a substantial subclass of strongly almost periodic point measures.…
Gegenstand der vorliegenden Arbeit ist die Konstruktion einer nichtkommutativen Transportmetrik, die es erlaubt, spursymmetrische vollständig Markovsche Halbgruppen als Gradientenfluss eines Entropiefunktionals aufzufassen. Eine vollständig Markovsche Halbgruppe ist eine Halbgruppe von unitalen, vollständig…
In this thesis we contribute to the spectral theory of hyperbolic surfaces. More concretely, we prove several results concerning the distibution of infinite-area hyperbolic surfaces. Most notable among them are a Weyl law and an improved fractal Weyl law for families of covers of Schottky surfaces, the…
Die vorliegende Arbeit beschäftigt sich mit Energieformen (energy forms). Eine Energieform ist eine unterhalbstetige quadratische Form auf dem Raum der reellwertigen, m-fast überall definierten Funktionen, welche einer messbaren Funktion f ihre Energie E(f) zuordnet und eine Kontraktionseigenschaft besitzt.…
Die vorliegende Arbeit befasst sich mit Stetigkeitseigenschaften der Spektren einer Operatorfamilie indiziert durch einen topologischen Raum. Speziell werden lineare beschränkte Operatoren betrachtet, die selbst-adjungiert, unitär bzw. normal sind. Der Abstand der zugehörigen Spektren wird durch die…
Non-smooth saddle-node bifurcations of one-parameter families of quasiperiodically driven dynamical systems on the real line give rise to strange non-chaotic attractors. In this thesis, we provide a class of families which has non-empty interior in the C2-topology and whose elements undergo non-smooth…
The present dissertation thesis is concerned with Banach space-valued convergence theorems along Folner type sequences in geometries with amenable structures. The text contains new ergodic theorems for groups, as well as an almost-additive and a subadditive convergence theorem for hyperfinite, weakly…
We study a class of rooted trees with a substitution type structure. These trees are not necessarily regular, but exhibit a lot of symmetries. We consider nearest neighbor operators which reflect the symmetries of the trees. The spectrum of such operators is proven to be purely absolutely continuous…