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In this thesis we solve the coboundary equation $delta c=d$ with bounds for cochains with values in a coherent subsheaf of some $mathcal{O}^p_{Omega}$, where $Omega$ is a Stein manifold. In particular the existence of a finite set of global generators is not assumed. Our result applies therefore to the ideal sheaf $mathcal{J}_Vsubset mathcal{O}_{C^N}$ of germs of holomorphic functions vanishing on a closed analytic submanifold $VsubsetC^N$. Although we are mainly interested in the estimates for the solutions of $delta c=d$, the techniques used also lead to a proof for the classical Theorem B of Cartan for coherent subsheafs of some $mathcal{O}^p_{Omega}$, avoiding the Mittag-Leffler argument. We derive an extension theorem for holomorphic functions on V to entire functions, with control on growth behaviour. ewline As a corollary we construct a linear tame extension operator $H(V)to H(C^N)$ under the hypothesis that H(V) is linear tamely isomorphic to the infinite type power series space $Lambda_infty(k^{frac{1}{n}})$, n= dim$_{C}V$; this condition is also necessary. Here the supnorms on H(V) are taken over intersections of V with polycylinders of polyradii e^m, $min N$. Aytuna asked how much, and what kind of, information about the complex analytic structure of V is carried by the Frechet space H(V). We prove that H(V) is linear tamely isomorphic to a power series space of infinite type if and only if V is algebraic.
Diese kurze Einfuehrung in Theorie und Berechnung linearer Rekurrenzen versucht, eine Luecke in der Literatur zu fuellen. Zu diesem Zweck sind viele ausfuehrliche Beispiele angegeben. This short introduction to theory and usage of linear recurrence
In Shive wave machines - Wave propagation, dispersion, reflection, simulation (arXiv:1503.02088) technical details of Shive wave machines are discussed. Wave propagation on these machines is simulated using the commercial numerical computing environm
We obtain sufficient conditions for a densely defined operator on the Fock space to be bounded or compact. Under the boundedness condition we then characterize the compactness of the operator in terms of its Berezin transform.
The corona problem was motivated by the question of the density of the open unit disk D in the maximal ideal space of the algebra, H1(D), of bounded holomorphic functions on D. In this note we study relationships of the problem with questions in oper
The Drury-Arveson space $H^2_d$, also known as symmetric Fock space or the $d$-shift space, is a Hilbert function space that has a natural $d$-tuple of operators acting on it, which gives it the structure of a Hilbert module. This survey aims to intr