Titlebook: Complex Analysis; A Functional Analysi D. H. Luecking,L. A. Rubel Textbook 1984 Springer-Verlag New York Inc. 1984 Analysis.Funktionalanaly

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Christian Büning,Constantin WirthIf f ∈ .(G), G a connected open set, it is a consequence of the power series expansion for holomorphic functions that if f(z.) = 0, z. → z. ∈ G then f = 0 in G. It is also a consequence that if f.(z.) = 0 for n = 0,1,2,…, then f = 0 in G. We adopt conventions about “sets with multiplicity” that allow us to treat both cases as one.

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Erste Hilfe bei Sportverletzungen,We use the results of the previous section to derive some descriptive results on ideals of holomorphic functions.

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Erste Hilfe bei Sportverletzungen,The Riemann Mapping Theorem implies that, as far as . can tell, all simply connected regions are the “same”. To clarify what this means we need the following notion of equivalence.

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https://doi.org/10.1007/978-3-030-67249-2This chapter is intended as a prerequisite for later chapters. In it we introduce a topology on the dual of a topological vector space. We present some of the standard results in the theory of Fréchet spaces and some additional results on topological vector spaces in general.

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Duality,The concept of duality is one of the most productive in analysis. One can very nearly characterize applications of functional analysis as applications of duality. Most of our goal in succeeding sections will be identifying the dual of .(G) and exploiting that identification. Toward this end, we begin with the definition.

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The Hahn-Banach Theorem, and Applications,A major tool in the application of duality results (in . locally convex topological vector space) is the Hahn-Banach Theorem. We state here one standard version (there are many equivalent versions) and two important corollaries.