LACUNARY SERIES AND INDEPENDENT FUNCTIONS

DOI10.1070/rm1966v021n06ABEH001196zbMath0178.06903WikidataQ56070037 ScholiaQ56070037MaRDI QIDQ5564490

V. F. Gaposhkin

Publication date: 1966

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

zbMATH Keywords

approximation and series expansion

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Study of almost everywhere convergence of series by mean of martingale methods ⋮ On the law of the iterated logarithm for trigonometric series with bounded gaps. II ⋮ On the central limit theorem for \(f(n_{k}x)\) ⋮ Pseudorandom processes ⋮ Strong approximation of lacunary series with random gaps ⋮ Lacunary sequences and conditional independence ⋮ Concentration inequalities and limit theorems for randomized sums ⋮ Khinchin's inequality for k-fold products of independent random variables ⋮ Statistical independence in mathematics -- the key to a Gaussian law ⋮ On the Uniform Theory of Lacunary Series ⋮ Almost everywhere convergence questions of series of translates of non-negative functions ⋮ Lacunary subsystems of the Walsh system of functions ⋮ From van der Corput to modern constructions of sequences for quasi-Monte Carlo rules ⋮ On the class of limits of lacunary trigonometric series ⋮ Summation of subsequences of partial sums of Fourier series ⋮ On certain properties of Rademacher chaos ⋮ Fourier-Laplace series on a sphere ⋮ Convergence systems and strong consistency of least squares estimates in regression models ⋮ Almost everywhere convergence of ergodic series ⋮ Metric Discrepancy Results for Sequences {nkx} and Diophantine Equations ⋮ The Sidon-Zygmund inequality in the theory of lacunary trigonometric series ⋮ Estimation of the moments of weighted sums for mixing processes ⋮ Moment inequalities and the strong laws of large numbers ⋮ Lacunary systems and generalized linear processes ⋮ On series \(\sum c_k f(kx)\) and Khinchin's conjecture ⋮ On superstrictly singular embeddings ⋮ Irregular LIL behaviour of lacunary trigonometric series ⋮ Generalization of the Steinhaus problem on the convergence of series with random signs ⋮ The law of the iterated logarithm for subsequences of random variables ⋮ GCD sums from Poisson integrals and systems of dilated functions ⋮ Law of iterated logarithm for lacunary series with respect to the Walsh system ⋮ Unconditional convergence and almost everywhere convergence ⋮ Rademacher functions in symmetric spaces ⋮ Some examples of application of the metric entropy method ⋮ On subsystems of systems of sets ⋮ Generalization of some classical inequalities in the theory of orthogonal series ⋮ Uniqueness theorem for series with gaps ⋮ Analytic description of statistics of spectra of quantum graphs ⋮ On trigonometric series and primitive functions ⋮ On the law of the iterated logarithm for permuted lacunary sequences ⋮ On the asymptotic behaviour of ?f(nkx) ⋮ On the asymptotic behaviour of ?f(nkx) ⋮ A central limit theorem for strongly multiplicative systems of functions ⋮ An extension of the Komlós subsequence theorem ⋮ Almost sure invariance principles for the empirical process of lacunary sequences ⋮ Lacunary series in multiplicative systems of functions. I ⋮ Lacunar series in multiplicative systems of functions. II ⋮ On independent and stationary subsystems of the Walsh system and periodic multiplicative systems ⋮ Extraction of subsystems ``majorized by the Rademacher system ⋮ Every sequence converging to 0 weakly in L\(_2\) contains an unconditional convergence sequence ⋮ Precise distribution properties of the van der Corput sequence and related sequences ⋮ Series with respect to the Walsh system and their generalizations ⋮ Lacunary Walsh series ⋮ Exchangeable random variables and the subsequence principle ⋮ On permutation-invariance of limit theorems ⋮ Lacunary entire functions ⋮ Orthonormal Banach systems with applications to linear processes ⋮ Extensions of the Menchoff-Rademacher theorem with applications to ergodic theory

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