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- Author or Editor: Michel Weber x
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Abstract
We give several applications of an identity for sums of weakly stationary sequences due to Ky Fan.
Summary
Let
Summary
By applying the majorizing measure method, we obtain a new estimate of the supremum of random trigonometric sums. We show that this estimate is strictly stronger than the well-known Salem-Zygmund's estimate, as well as recent general formulations of it obtained by the author. This improvement is obtained by considering the case when the characters are indexed on sub-exponentially growing sequences of integers. Several remarkable examples are studied.
Abstract
Let f(n) be a strongly additive complex-valued arithmetic function. Under mild conditions on f, we prove the following weighted strong law of large numbers: if X,X
1,X
2, … is any sequence of integrable i.i.d. random variables, then