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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Nel mathematical field of complex analysis, Akhiezer's theorem is a result about entire functions proved by Naum Akhiezer.[1]
Dichiarazione[]
Permettere f(z) be an entire function di exponential type t, insieme a f(X) ≥ 0 for real X. Then the following are equivalent:
- There exists an entire function F, di exponential type t/2, having all its zeros in the (Chiuso) upper half plane, tale che
!["{stile]("https://wikimedia.org/api/rest_v1/media/math/render/svg/ca8ad8ebc444c9cb2c87065e191a46513a2b4ca3")
- Uno ha:
!["{displaystyle]("https://wikimedia.org/api/rest_v1/media/math/render/svg/74e4c073ef0bd4977ab5d522165a5be625c2ede1")
dove zn are the zeros of f.
Risultati correlati[]
It is not hard to show that the Fejér–Riesz theorem is a special case.[2]
Appunti[]
- ^ vedere Akhiezer (1948).
- ^ vedere Boas (1954) e Boas (1944) for references.
Riferimenti[]
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", Duca Matematica. J., 11: 9–15, doi:10.1215/s0012-7094-44-01102-6, ISSN 0012-7094
- Akhiezer, N. io. (1948), "On the theory of entire functions of finite degree", Doklady Akademii Nauk SSSR, Nuova serie, 63: 475–478, SIG 0027333
Se vuoi conoscere altri articoli simili a Akhiezer's theorem puoi visitare la categoria Teoremi in analisi complessa.
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