منابع مشابه
On Bounded Analytic Functions
The objective of this paper is to give an alternative derivation of results on bounded analytic functions recently obtained by Ahlfors [l] and Garabedian [2].1 While it is admitted that the main idea to be used is more in the nature of a lucky guess than of a method, it will be found that the gain in brevity and simplicity of the argument is considerable. As a by-product, we shall also obtain a...
متن کاملBounded Analytic Functions
If D is a domain in the complex s-plane, then the family B=B(D) of bounded analytic functions in D is defined as consisting of those analytic functions ƒ(z) which are regular and single-valued in D and which satisfy the inequality \f(z) | < 1 at all points of D. The classical investigations of the family B(D) were restricted to the case in which D is a simply-connected domain. In fact, D was ge...
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In this paper we study the Hilbert space of analytic functions with finite Dirichlet integral in a connected open set C2 in the complex plane. We show that every such function can be represented as a quotient of two bounded analytic functions, each of which has a finite Dirichlet integral. This has several consequences for the structure of invariant subspaces of the algebra of multiplication op...
متن کاملOn Certain Analytic Functions of Bounded Boundary Rotation
In this paper we introduce certain analytic functions of boundary rotation bounded by k1r which are of Caratheodory origin. With them we study two classes of analytic and univalent functions in the unit disk E = {z E C Izi < I} , which are also of bounded boundary rotation.
متن کاملNote on Functions Bounded and Analytic in the Unit Circle1
W. Gross [l ] was the first to give an example of an entire function w=<p(f) with the property that, for each complex number w, there exists an uncountable set of asymptotic paths along which <p(f) tends to w. We shall consider, in this note, the corresponding problem for functions analytic in the unit circle, U: \z\ < 1. Let <p(f) be the entire function constructed by Gross, and let L be one o...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1950
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1950-0034457-3