On the theorem of Ivasev-Musatov. I

Thomas-William Korner

Annales de l'institut Fourier (1977)

  • Volume: 27, Issue: 3, page 97-115
  • ISSN: 0373-0956

Abstract

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We give a new version of Ivasev-Musatov’s construction of a measure whose support has Lebesgue measure zero but whose Fourier transform drops away extremely rapidly.

How to cite

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Korner, Thomas-William. "On the theorem of Ivasev-Musatov. I." Annales de l'institut Fourier 27.3 (1977): 97-115. <http://eudml.org/doc/74332>.

@article{Korner1977,
abstract = {We give a new version of Ivasev-Musatov’s construction of a measure whose support has Lebesgue measure zero but whose Fourier transform drops away extremely rapidly.},
author = {Korner, Thomas-William},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {3},
pages = {97-115},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the theorem of Ivasev-Musatov. I},
url = {http://eudml.org/doc/74332},
volume = {27},
year = {1977},
}

TY - JOUR
AU - Korner, Thomas-William
TI - On the theorem of Ivasev-Musatov. I
JO - Annales de l'institut Fourier
PY - 1977
PB - Association des Annales de l'Institut Fourier
VL - 27
IS - 3
SP - 97
EP - 115
AB - We give a new version of Ivasev-Musatov’s construction of a measure whose support has Lebesgue measure zero but whose Fourier transform drops away extremely rapidly.
LA - eng
UR - http://eudml.org/doc/74332
ER -

References

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  1. [1] O.S. IVAŠEV-MUSATOV, On the Fourier-Stieljes coefficients of singular functions, Dokl. Akad. Nauk SSSR (N.S.), 82 (1952), 9-11. (Russian). Zbl0046.06703
  2. [2] O.S. IVAŠEV-MUSATOV, On Fourier-Stieljes coefficients of singular functions, Izv. Akad. Nauk SSSR., Ser. Mat., 20 (1956), 179-196. (Russian). English translation in Amer. Math. Soc. Translations, Series 2, 10 (1958), 107-124. Zbl0093.07004
  3. [3] O.S. IVAŠEV-MUSATOV, On the coefficients of trigonometric nul series, Izv. Akad. Nauk SSSR., Ser. Nat., 21 (1957), 559-578. (Russian). English translation in Amer. Math. Soc. Translations, Series 2, 14 (1960), 289-310. Zbl0094.27101MR20 #5392
  4. [4] J.-P. KAHANE and R. SALEM, Ensembles Parfaits et Séries Trigonométriques, Hermann Paris (1963). Zbl0112.29304MR28 #3279
  5. [5] A. ZYGMUND, Trigonometric Series, Vols. I. & II., Cambridge (1959). Zbl0085.05601

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