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On Linear Functionals of Rational Type over H (ID)
Author(s) -
Fournier Richard
Publication year - 1995
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19951730111
Subject(s) - mathematics , characterization (materials science) , type (biology) , convergence (economics) , unit disk , topology (electrical circuits) , compact space , complex plane , linear space , space (punctuation) , set (abstract data type) , unit (ring theory) , plane (geometry) , function (biology) , pure mathematics , discrete mathematics , mathematical analysis , combinatorics , geometry , computer science , ecology , materials science , mathematics education , evolutionary biology , economics , nanotechnology , biology , programming language , economic growth , operating system
Abstract Let H (ID) denote the set of analytic functions in the unit disk ID of the complex plane, endowed with the topology of uniform convergence on compact subsets of ID. Let Λ denote the space of continuous linear functionals over H (ID). In this paper we obtain a characterization of those λ ∈Λ such that\documentclass{article}\pagestyle{empty}\begin{document} $ \lambda (z^k B(z)) = 0 for k = 0,1,2,\ldots, $\end{document}where B is a fixed function in H (ID). We also include a discussion of the sharpness of this characterization and an application to some extremal problem concerning Λ.