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Mathematik für Informatik und BioInformatik ist eine speziell auf das Informatik- und BioInformatik-Studium zugeschnittene breite Einführung in die Mathematik im Umfang der ersten drei bis vier Semester an Universitäten. Der klassische Stoff von Analysis und Linearer Algebra ist auf das wirklich Wesentliche konzentriert. Zusätzlich enthalten sind speziell für Informatik und BioInformatik wichtige...
Let T be a Markov operator on an L¹-space. We study conditions under which T is mean ergodic and satisfies dim Fix(T) < ∞. Among other things we prove that the sequence $(n^{-1} ∑_{k=0}^{n-1} T^k)ₙ$ converges strongly to a rank-one projection if and only if there exists a function 0 ≠ h ∈ L¹₊ which satisfies $lim_{n→∞} ||(h - n^{-1} ∑_{k=0}^{n-1} T^k f)₊|| = 0$ for every density f. Analogous results...
Let X be a Banach space over ℂ. The bounded linear operator T on X is called quasi-constricted if the subspace $X₀: = {x ∈ X: lim_{n→ ∞} ||Tⁿx|| = 0}$ is closed and has finite codimension. We show that a power bounded linear operator T ∈ L(X) is quasi-constricted iff it has an attractor A with Hausdorff measure of noncompactness $χ_{||·||₁}(A) < 1$ for some equivalent norm ||·||₁ on X. Moreover,...
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