The value-distribution of lacunary series and a conjecture of Paley

Takafumi Murai

Annales de l'institut Fourier (1981)

  • Volume: 31, Issue: 1, page 135-156
  • ISSN: 0373-0956

Abstract

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The purpose of this paper is to establish a theorem which answers a conjecture of Paley on the distribution of values of Hadamard lacunary series and which is useful to study the Peano curve property of such series.

How to cite

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Murai, Takafumi. "The value-distribution of lacunary series and a conjecture of Paley." Annales de l'institut Fourier 31.1 (1981): 135-156. <http://eudml.org/doc/74478>.

@article{Murai1981,
abstract = {The purpose of this paper is to establish a theorem which answers a conjecture of Paley on the distribution of values of Hadamard lacunary series and which is useful to study the Peano curve property of such series.},
author = {Murai, Takafumi},
journal = {Annales de l'institut Fourier},
keywords = {Hadamard lacunary series; Peano curve},
language = {eng},
number = {1},
pages = {135-156},
publisher = {Association des Annales de l'Institut Fourier},
title = {The value-distribution of lacunary series and a conjecture of Paley},
url = {http://eudml.org/doc/74478},
volume = {31},
year = {1981},
}

TY - JOUR
AU - Murai, Takafumi
TI - The value-distribution of lacunary series and a conjecture of Paley
JO - Annales de l'institut Fourier
PY - 1981
PB - Association des Annales de l'Institut Fourier
VL - 31
IS - 1
SP - 135
EP - 156
AB - The purpose of this paper is to establish a theorem which answers a conjecture of Paley on the distribution of values of Hadamard lacunary series and which is useful to study the Peano curve property of such series.
LA - eng
KW - Hadamard lacunary series; Peano curve
UR - http://eudml.org/doc/74478
ER -

References

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  1. [1] J.M. ANDERSON, Boundary properties of analytic functions with gap power series, Quart. J. Math. Oxford, (2) 21 (1970), 247-256. Zbl0209.37801
  2. [2] K.G. BINMORE, R. HORNBLOWER, Boundary behaviour of functions with Hadamard gaps, Nagoya Math. J., 48 (1972), 173-181. Zbl0244.30029MR47 #7036
  3. [3] I.L. CHANG, On the zeros of power series with Hadamard Gaps-Distribution in sectors, Trans. of the Amer. Math. Soc., 178 (1973), 393-400. Zbl0229.30009MR47 #3646
  4. [4] W.H.J. FUCHS, On the zeros of power series with Hadamard gaps, Nagoya Math. J., 29 (1967), 167-174. Zbl0172.36902MR35 #1780
  5. [5] W.H.J. FUCHS, Topics in Nevanlinna theory, Proc. NRL Conference on classical function theory, Math. Rec. Center, Naval Research Laboratory, Washington, D.C., 1970, 1-32. Zbl0294.30021MR48 #11511
  6. [6] J.P. KAHANE, Lacunary Taylor and Fourier series, Bull. Amer. Math. Soc., 70 (1964), 199-213. Zbl0121.30102MR29 #223
  7. [7] J.P. KAHANE, G. WEISS, M. WEISS, On lacunary power series, Arkiv för Math., B.5 No 1 (1963), 1-26. Zbl0134.05701MR32 #7716
  8. [8] T. MURAI, Sur la distribution des valeurs des séries lacunaires, J. of the London Math. Soc. (2), 21 (1980), 93-110. Zbl0449.30017MR81g:30004
  9. [9] T. MURAI, Une conjecture de Paley sur séries de Taylor lacunaires, C.R.A.S., Paris, t. 290 (2 juin 1980), 947-948. Zbl0443.30001MR81j:30006
  10. [10] R.E.A.C. PALEY, On lacunary power series, Proc. Nat. Acad. Sci. U.S.A., 19 (1933), 271-272. Zbl0006.19705JFM59.0320.03
  11. [11] R. SALEM, A. ZYGMUND, Lacunary power series and Peano curves, Duke J. of Math., 12 (1945), 569-578. Zbl0060.20402MR7,378c
  12. [12] M. WEISS, Concerning a theorem of Paley on lacunary trigonometric series, Acta Math., 102 (1959), 225-238. Zbl0091.06702MR22 #8109
  13. [13] G. WEISS, M. WEISS, On the Picard property of lacunary power series, Studia Math., 22 (1963), 221-245. Zbl0111.27202MR26 #2588
  14. [14] A. ZYGMUND, Trigonometric series I, II, Cambridge, 1959. Zbl0085.05601

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