| 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:
|
http://hdl.handle.net/10338.dmlcz/103253 |
| . |
| 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 |
| . |
