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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No mathematical field of complex analysis, Akhiezer's theorem is a result about entire functions proved by Naum Akhiezer.[1]
Declaração[]
Deixar f(z) be an entire function do exponential type t, com f(x) ≥ 0 for real x. Then the following are equivalent:
- There exists an entire function F, do exponential type t/2, having all its zeros in the (fechado) upper half plane, de tal modo que
!["{estilo]("https://wikimedia.org/api/rest_v1/media/math/render/svg/ca8ad8ebc444c9cb2c87065e191a46513a2b4ca3")
- Um tem:
!["{displaystyle]("https://wikimedia.org/api/rest_v1/media/math/render/svg/74e4c073ef0bd4977ab5d522165a5be625c2ede1")
Onde zn are the zeros of f.
Resultados relacionados[]
It is not hard to show that the Fejér–Riesz theorem is a special case.[2]
Notas[]
- ^ Vejo Akhiezer (1948).
- ^ Vejo Boas (1954) e Boas (1944) for references.
Referências[]
Boas, Jr., Ralph Philip (1954), Entire functions, Nova york: Academic Press Inc., pp. 124–132
- Boas, Jr., R. P. (1944), "Functions of exponential type. I", Duque Matemática. J., 11: 9-15, doi:10.1215/s0012-7094-44-01102-6, ISSN 0012-7094
- Akhiezer, N. EU. (1948), "On the theory of entire functions of finite degree", Doklady Akademii Nauk SSSR, Nova série, 63: 475-478, MR 0027333
Se você quiser conhecer outros artigos semelhantes a Akhiezer's theorem você pode visitar a categoria Theorems in complex analysis.
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