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Title: On the decomposition of a positive real function into positive real summands (English)
Author: Gregor, Jiří
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 14
Issue: 6
Year: 1969
Pages: 429-441
Summary lang: English
Summary lang: Czech
Category: math
Summary: Analytic functions of one variable with positive real part in the right half-plane, assuming real values on the real positive half-axis, are called positive real functions. In the paper necessary and sufficient conditions for a positive real function to be a sum of two positive real functions are given. Further the structure of any positive real function $f$ is shown when written in the form $f=f_0+g+h$ where $f_0,g,h$ are positive real functions and $f_0$ has all the pure imaginary poles of the function $f$. (English)
Keyword: complex functions
MSC: 30-65
idZBL: Zbl 0193.36803
idMR: MR0249634
DOI: 10.21136/AM.1969.103253
Date available: 2008-05-20T17:46:26Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] Achiezer N. I.: Классическая проблема моментов.GIFML, Moscow 1961.
Reference: [2] Pondělíček В.: Примечание к преобразованию Ричардса.Acta Polytechnica, III (1967), 1, pp. 27--34.
Reference: [3] Richards P.: A Special Class of Functions with Positive Real part in a Half-plane.Duke Math. J., 148 (1947), pp. 122-145. MR 0022261
Reference: [4] Šulista M.: Brunesche Functionen.Acta Polytechnica, IV (1964), 2, pp. 23-74.
Reference: [5] Valiron G.: Fonctions analytiques.Paris 1954 (the translation into russian: Аналитические функции, GITTL, Moscow 1957 was used). Zbl 0055.06702, MR 0061658


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