Certain lacunary cosine series are recurrent

• Autorzy: D. J. Grubb , Charles N. Moore
• Języki publikacji: EN

Abstrakty

EN

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

Kategorie tematyczne

• 42A55: Lacunary series of trigonometric and other functions; Riesz products

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994
• Tom: 108
• Numer: 1
• Strony: 21-23

Daty

wydano

1994

otrzymano

1992-04-07

Twórcy

autor

D. J. Grubb

• Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115, U.S.A.

autor

Charles N. Moore

• Department Of Mathematics, Kansas State University, Manhattan, Kansas 66506, U.S.A.

Bibliografia

• [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.
• [2] J. M. Anderson and L. D. Pitt, On recurrence properties of certain lacunary series, II. The series $∑_1^n exp(ia^nθ)$, ibid., 83-96.
• [3] D. A. Brannan and W. K. Hayman, Research problems in complex analysis, Bull. London Math. Soc. 21 (1989), 1-35.
• [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.