# Certain lacunary cosine series are recurrent

Studia Mathematica (1994)

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

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topGrubb, 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

top- [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] J. M. Anderson and L. D. Pitt, On recurrence properties of certain lacunary series, II. The series ${\sum}_{1}^{n}exp\left(i{a}^{n}\theta \right)$, ibid., 83-96.
- [3] D. A. Brannan and W. K. Hayman, Research problems in complex analysis, Bull. London Math. Soc. 21 (1989), 1-35. Zbl0695.30001
- [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] D. Ullrich, Recurrence for lacunary cosine series, preprint.
- [6] A. Zygmund, Trigonometric Series, 2nd ed., Cambridge Univ. Press, 1959. Zbl0085.05601

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