Strong approximations on lacunary trigonometric series with weights. (English) Zbl 0654.42015
Philipp and Stount established the almost sure principle for lacunary trigonometric series with unweighted summands and stated that the approximate order might be close to 1/3. The proof of the sharpness of the approximate order close to 1/3 was given recently by Zhigang. The author of the present paper improves the result of Zhigang and obtains the best possible order as 1/4. Further the author discusses the general case of lacunary trigonometric series with weights and obtains the logarithmic order in some particular cases.
Reviewer: D.Somasundaram
MSC:
42A55 | Lacunary series of trigonometric and other functions; Riesz products |