# 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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topGregor, 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

top- Achiezer N. I., Классическая проблема моментов, GIFML, Moscow 1961. (1961)
- Pondělíček В., Примечание к преобразованию Ричардса, Acta Polytechnica, III (1967), 1, pp. 27--34. (1967)
- 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
- Šulista M., Brunesche Functionen, Acta Polytechnica, IV (1964), 2, pp. 23-74. (1964)
- Valiron G., Fonctions analytiques, Paris 1954 (the translation into russian: Аналитические функции, GITTL, Moscow 1957 was used). (1954) Zbl0055.06702MR0061658

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