The deficiency of entire functions with Fejér gaps

Takafumi Murai

Annales de l'institut Fourier (1983)

  • Volume: 33, Issue: 3, page 39-58
  • ISSN: 0373-0956

Abstract

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We say that an entire function f ( z ) = ∑ k = 0 a k z n k ( 0 = n 0 < n 1 < n 2 < ... ) has Fejér gaps if ∑ k = 1 ∞ 1 / n k < ∞ . The main result of this paper is as follows: An entire function with Fejér gaps has no finite deficient value.

How to cite

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Murai, Takafumi. "The deficiency of entire functions with Fejér gaps." Annales de l'institut Fourier 33.3 (1983): 39-58. <http://eudml.org/doc/74600>.

@article{Murai1983,
abstract = {We say that an entire function $f(z)=\sum _\{k=0\}a_kz^\{n_k\}~(0=n_0&lt; n_1&lt; n_2&lt; \ldots )$ has Fejér gaps if $\sum ^\infty _\{k=1\}1/n_k&lt; \infty .$ The main result of this paper is as follows: An entire function with Fejér gaps has no finite deficient value.},
author = {Murai, Takafumi},
journal = {Annales de l'institut Fourier},
keywords = {deficiency; Fejer gap; Fabry gap},
language = {eng},
number = {3},
pages = {39-58},
publisher = {Association des Annales de l'Institut Fourier},
title = {The deficiency of entire functions with Fejér gaps},
url = {http://eudml.org/doc/74600},
volume = {33},
year = {1983},
}

TY - JOUR
AU - Murai, Takafumi
TI - The deficiency of entire functions with Fejér gaps
JO - Annales de l'institut Fourier
PY - 1983
PB - Association des Annales de l'Institut Fourier
VL - 33
IS - 3
SP - 39
EP - 58
AB - We say that an entire function $f(z)=\sum _{k=0}a_kz^{n_k}~(0=n_0&lt; n_1&lt; n_2&lt; \ldots )$ has Fejér gaps if $\sum ^\infty _{k=1}1/n_k&lt; \infty .$ The main result of this paper is as follows: An entire function with Fejér gaps has no finite deficient value.
LA - eng
KW - deficiency; Fejer gap; Fabry gap
UR - http://eudml.org/doc/74600
ER -

References

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  2. [2] M. BIERNACKI, Sur les fonctions entières à séries lacunaires, C.R.A.S., Paris, Sér. A-B, 187 (1928), 477-479. Zbl54.0349.02JFM54.0349.02
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  11. [11] T. MURAI, The deficiency of gap series, Analysis (1983) to appear. Zbl0533.30028
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  15. [15] A. WIMAN, Über den Zusammenhang zwischen dem Maximalbetrage einer analytischen Function und dem grössten Gliede der zugehörigen Taylorschen Reihe, Acta Math., 37 (1914), 305-326. Zbl45.0641.02JFM45.0641.02
  16. [16] A. ZYGMUND, Trigonometric series I, Cambridge, 1959. Zbl0085.05601

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