Certain lacunary cosine series are recurrent

D. Grubb; Charles Moore

Studia Mathematica (1994)

  • Volume: 108, Issue: 1, page 21-23
  • ISSN: 0039-3223

Abstract

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Let the coefficients of a lacunary cosine series be bounded and not square-summable. Then the partial sums of the series are recurrent.

How to cite

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Grubb, D., and Moore, Charles. "Certain lacunary cosine series are recurrent." Studia Mathematica 108.1 (1994): 21-23. <http://eudml.org/doc/216037>.

@article{Grubb1994,
abstract = {Let the coefficients of a lacunary cosine series be bounded and not square-summable. Then the partial sums of the series are recurrent.},
author = {Grubb, D., Moore, Charles},
journal = {Studia Mathematica},
keywords = {partial sums; lacunary cosine series},
language = {eng},
number = {1},
pages = {21-23},
title = {Certain lacunary cosine series are recurrent},
url = {http://eudml.org/doc/216037},
volume = {108},
year = {1994},
}

TY - JOUR
AU - Grubb, D.
AU - Moore, Charles
TI - Certain lacunary cosine series are recurrent
JO - Studia Mathematica
PY - 1994
VL - 108
IS - 1
SP - 21
EP - 23
AB - Let the coefficients of a lacunary cosine series be bounded and not square-summable. Then the partial sums of the series are recurrent.
LA - eng
KW - partial sums; lacunary cosine series
UR - http://eudml.org/doc/216037
ER -

References

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  1. [1] J. M. Anderson and L. D. Pitt, On recurrence properties of certain lacunary series. I. General results, J. Reine Angew. Math. 377 (1987), 65-82. Zbl0603.30004
  2. [2] J. M. Anderson and L. D. Pitt, On recurrence properties of certain lacunary series, II. The series ∑ 1 n e x p ( i a n θ ) , ibid., 83-96. 
  3. [3] D. A. Brannan and W. K. Hayman, Research problems in complex analysis, Bull. London Math. Soc. 21 (1989), 1-35. Zbl0695.30001
  4. [4] T. Murai, Gap series, in: Analytic Function Theory of One Complex Variable, Y. Komatu, K. Niino and C. Yang (eds.), Pitman Res. Notes in Math. 212, Longman Scientific & Technical, New York, 1989, 149-177. 
  5. [5] D. Ullrich, Recurrence for lacunary cosine series, preprint. 
  6. [6] A. Zygmund, Trigonometric Series, 2nd ed., Cambridge Univ. Press, 1959. Zbl0085.05601

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