Berkes, István (2017) On the uniform theory of lacunary series. In: Number Theory  Diophantine Problems, Uniform Distribution and Applications: Festschrift in Honour of Robert F. Tichy's 60th Birthday. Springer International Publishing, Cham, pp. 137167. ISBN 9783319553573

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Abstract
The theory of lacunary series starts with Weierstrass' famous example (1872) of a continuous, nondifferentiable function and now we have a wide and nearly complete theory of lacunary subsequences of classical orthogonal systems, as well as asymptotic results for thin subsequences of general function systems. However, many applications of lacunary series in harmonic analysis, orthogonal function theory, Banach space theory, etc. require uniform limit theorems for such series, i.e., theorems holding simultaneously for a class of lacunary series, and such results are much harder to prove than dealing with individual series. The purpose of this paper is to give a survey of uniformity theory of lacunary series and discuss new results in the field. In particular, we study the permutationinvariance of lacunary series and their connection with Diophantine equations, uniform limit theorems in Banach space theory, resonance phenomena for lacunary series, lacunary sequences with random gaps, and the metric discrepancy theory of lacunary sequences. © 2017. Springer International Publishing AG.
Item Type:  Book Section 

Uncontrolled Keywords:  Orthogonal functions; Resonance phenomena; Orthogonal systems; Nondifferentiable functions; Lacunary sequences; Discrepancy theory; Diophantine equation; Banach space theory; Asymptotic results; Banach Spaces 
Subjects:  H Social Sciences / társadalomtudományok > HA Statistics / statisztika 
SWORD Depositor:  MTMT SWORD 
Depositing User:  MTMT SWORD 
Date Deposited:  11 Sep 2018 12:55 
Last Modified:  11 Sep 2018 12:55 
URI:  http://real.mtak.hu/id/eprint/83525 
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