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- Author or Editor: Michel Weber x
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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
We give several applications of an identity for sums of weakly stationary sequences due to Ky Fan.
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