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Keywords:
complex functions
complex functions
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 $f$.
References:
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[2] Pondělíček В.: Примечание к преобразованию Ричардса. Acta Polytechnica, III (1967), 1, pp. 27--34.
[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
[4] Šulista M.: Brunesche Functionen. Acta Polytechnica, IV (1964), 2, pp. 23-74.
[5] Valiron G.: Fonctions analytiques. Paris 1954 (the translation into russian: Аналитические функции, GITTL, Moscow 1957 was used). MR 0061658 | Zbl 0055.06702
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