G N5 A practical introduction. A major focus is extension phenomena alien to the one-dimensional theory, which are expressed in the famous Hartog's Kugelsatz, the theorem of Cartan-Thullen, and Bochner's theorem. We also show that there is an entire holomorphic curve in Hilbert space on which there is a bounded holomorphic function on the trace of a ball that has no bounded holomorphic extension to even a smaller concentric ball. We introduce a class of analytic sheaves in a Banach space X, that we shall call cohesive sheaves. In particular, in the first result above, it is not enough to assume that f is merely continuous, rather than Lipschitz continuous. We also give an application concerning neighborhoods of complex submanifolds.
Canadian Geodynamics Subcommittee Second report. The book primarily aims at students starting to work in the field of complex analysis in several variables and teachers who want to prepare a course. French, part 40 N This file contains citations beginning with the letter N. Committee on Research N277r Priorities in Tropical Biology Research priorities in tropical biology. We also prove an analog of Hefer's lemma, i. For a large class of Banach spaces X we prove the following. The properties addressed in the chapter are generalized to larger classes of locally convex spaces with Schauder basis including Banach spaces.
Let X be a Banach space with a countable unconditional basis e. As a consequence we find that the sheaf cohomology group Hq X,O vanishes if X has the bounded approximation property i. It is well known that in a Banach space E there are no substitute to the Lebesgue measure that means there does not exist a measure invariant by translations or rotations. Accordingly, we prove the analog of Cartan's Theorems A and B for cohesive sheaves over pseudoconvex open subsets of X, provided X has an unconditional basis. We also prove a vanishing theorem for a fairly general class of analytic sheaves over pseudoconvex open sets of a large class of Banach spaces.
N842f Farm and village production systems in the semi-arid tropics of West Africa. This page was last updated on 8-30-2000. Associate Committee N277s on Geodesy and Geophysics. Ed The fifty-third chapter of Isaiah. Holomorphic mean Lipschitz space in the open unit ball of C n is introduced. Many cross-references to other parts of mathematics, such as functional analysis or algebras, are pointed out in order to broaden the view and the understanding of the chosen topics.
It clearly focusses on special topics in complex analysis rather than trying to encompass as much material as possible. This chapter describes approximation of plurisubharmonic functions. First Kajiwara then Leiterer gave geometric or cohomological criteria in the spirit of the Grauert—Oka principle for an open subset D of a Stein manifold M to be itself Stein. Using the same technique we also prove that a form of Runge approximation better than an error function is not always possible. We study the completion problem to an invertible operator-valued function for the class of bounded holomorphic functions on the unit disk D C S with relatively compact images in the space of bounded linear operators between complex Banach spaces. Our main result is Theorem 3.
Lastly, we prove an interpolation result. La cohésion généralise l'idée de cohérence en dimension finie. There has been good progress on such Banach manifolds, due mainly to the work of Lempert and some of his students see, e. Since the class of Stein manifolds has not yet been generalized to complex Banach manifolds characterized by some inherent abstract conditions, and since the proof of Leiterer begins by embedding Stein manifolds in complex Euclidean space, we just look instead at the class of closed split complex Banach submanifolds of pseudoconvex open subsets of Banach spaces with an unconditional basis. Comments about this homepage welcome to.
We show that on some open sets, more general than balls, Runge approximation is possible in certain Banach spaces, and also in certain complex Banach manifolds. Let X be a Banach space with a countable unconditional basis e. We also give a few applications. This has many applications to analytic cohomology of complex Banach manifolds. O-E denote the ideal of germs of holomorphic functions on Omega that vanish on M resp.
This book gives a comprehensive introduction to complex analysis in several variables. In particular, we prove that in this class of functions the operator-valued corona problem and the completion problem are not equivalent, and establish an Oka-type principle asserting that the completion problem is solvable if and only if it is solvable in the class of continuous operator-valued functions on D with relatively compact images. Archaeological Survey of N277r Canada Research report. We give here criteria analogous to Leiterer's, e. RésuméOn introduit une classe de faisceaux analytiques dans un espace de Banach complexe X, que nous appelons faisceaux cohésifs.