# On the decomposition of a positive real function into positive real summands

Aplikace matematiky (1969)

• Volume: 14, Issue: 6, page 429-441
• ISSN: 0862-7940

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## Abstract

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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 $f$.

## How to cite

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Gregor, Jiří. "On the decomposition of a positive real function into positive real summands." Aplikace matematiky 14.6 (1969): 429-441. <http://eudml.org/doc/14618>.

@article{Gregor1969,
abstract = {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 $f$.},
author = {Gregor, Jiří},
journal = {Aplikace matematiky},
keywords = {complex functions},
language = {eng},
number = {6},
pages = {429-441},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the decomposition of a positive real function into positive real summands},
url = {http://eudml.org/doc/14618},
volume = {14},
year = {1969},
}

TY - JOUR
AU - Gregor, Jiří
TI - On the decomposition of a positive real function into positive real summands
JO - Aplikace matematiky
PY - 1969
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 14
IS - 6
SP - 429
EP - 441
AB - 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 $f$.
LA - eng
KW - complex functions
UR - http://eudml.org/doc/14618
ER -

## References

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1. Achiezer N. I., Классическая проблема моментов, GIFML, Moscow 1961. (1961)
2. Pondělíček В., Примечание к преобразованию Ричардса, Acta Polytechnica, III (1967), 1, pp. 27--34. (1967)
3. Richards P., A Special Class of Functions with Positive Real part in a Half-plane, Duke Math. J., 148 (1947), pp. 122-145. (1947) MR0022261
4. Šulista M., Brunesche Functionen, Acta Polytechnica, IV (1964), 2, pp. 23-74. (1964)
5. Valiron G., Fonctions analytiques, Paris 1954 (the translation into russian: Аналитические функции, GITTL, Moscow 1957 was used). (1954) Zbl0055.06702MR0061658

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