Akhiezer's theorem
In the mathematical field of complex analysis, Akhiezer's theorem is a result about entire functions proved by Naum Akhiezer.[1]
Akhiezer's theorem
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In dem mathematical field of complex analysis, Akhiezer's theorem is a result about entire functions proved by Naum Akhiezer.[1]
Aussage[]
Lassen f(z) be an entire function von exponential type t, mit f(x) ≥ 0 for real x. Then the following are equivalent:
- There exists an entire function F, von exponential type t/2, having all its zeros in the (abgeschlossen) upper half plane, so dass
!["{Anzeigestil]("https://wikimedia.org/api/rest_v1/media/math/render/svg/ca8ad8ebc444c9cb2c87065e191a46513a2b4ca3")
- Hat man:
!["{displaystyle]("https://wikimedia.org/api/rest_v1/media/math/render/svg/74e4c073ef0bd4977ab5d522165a5be625c2ede1")
wo zn are the zeros of f.
Verwandte Ergebnisse[]
It is not hard to show that the Fejér–Riesz theorem is a special case.[2]
Anmerkungen[]
- ^ sehen Akhiezer (1948).
- ^ sehen Boas (1954) und Boas (1944) for references.
Verweise[]
Boas, Jr., Ralph Philip (1954), Entire functions, New York: Academic Press Inc., pp. 124–132
- Boas, Jr., R. P. (1944), "Functions of exponential type. I", Herzog Math. J., 11: 9–15, doi:10.1215/s0012-7094-44-01102-6, ISSN 0012-7094
- Akhiezer, N. ich. (1948), "On the theory of entire functions of finite degree", Doklady Akademii Nauk SSSR, Neue Serien, 63: 475–478, HERR 0027333
Wenn Sie andere ähnliche Artikel wissen möchten Akhiezer's theorem Sie können die Kategorie besuchen Theoreme in der komplexen Analysis.
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