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  1. Diophantine conditions in the law of the iterated logarithm for lacunary systems

    It is a classical observation that lacunary function systems exhibit many properties which are typical for systems of independent random variables....

    Christoph Aistleitner, Lorenz Frühwirth, Joscha Prochno in Probability Theory and Related Fields
    Article Open access 03 April 2024

  2. A New Paranormed Sequence Space and Invariant Means

    The purpose of this paper is to introduce the new sequence space which emerges naturally from the concept of invariant means and lacunary sequence....
    Ekrem Savaş in Mathematics and Computation
    Conference paper 2023

  3. The large deviation behavior of lacunary sums

    Lorenz Frühwirth, Michael Juhos, Joscha Prochno in Monatshefte für Mathematik
    Article Open access 24 June 2022

  4. Lacunary statistical boundedness on time scales

    In this paper, we introduce the concept of lacunary statistical boundedness of Δ-measurable real-valued functions on an arbitrary time scale. We also...

    Bayram Sözbir, Selma Altundağ in Advances in Difference Equations
    Article Open access 04 December 2021

  7. Asymptotically Wijsman lacunary sequences of order \((\alpha ,\beta )\)

    Ravi Kumar, Sunil K. Sharma, Ajay K. Sharma in The Journal of Analysis
    Article 23 June 2023

  8. Infinite co-minimal pairs involving lacunary sequences and generalisations to higher dimensions

    In 2011, Nathanson proposed several questions on minimal complements in a group or a semigroup. The notion of minimal complements and being a minimal...

    Arindam Biswas, Jyoti Prakash Saha in The Ramanujan Journal
    Article 26 June 2021

  9. Lacunary eta-quotients modulo powers of primes

    An integral power series is called lacunary modulo M if almost all of its coefficients are divisible by M . Motivated by the parity problem for the...

    Tessa Cotron, Anya Michaelsen, ... Weitao Zhu in The Ramanujan Journal
    Article 18 July 2020

  10. Extraction of Lacunary Subsystems

    By using results of the previous chapter, we obtain here necessary and sufficient conditions, under which an arbitrary sequence of r.v.’s contains a...
    Sergey V. Astashkin in The Rademacher System in Function Spaces
    Chapter 2020

  11. Paley’s Inequality for Discrete Groups

    This article studies Paley’s theory of lacunary Fourier series for von Neumann algebra of discrete groups. The results unify and generalize the work...

    Chian Yeong Chuah, Yazhou Han, ... Tao Mei in Journal of Fourier Analysis and Applications
    Article 26 September 2022

  13. Lacunary Statistical Convergence of Order \(\alpha \) for Generalized Difference Sequences and Summability Through Modulus Function

    In this paper, we define the space \(S_\theta ^\alpha (\Delta _v^m)\) of all \(\Delta _v^m\)-lacunary statistical convergent sequences of order...
    A. K. Verma, Sudhanshu Kumar in Mathematical Analysis I: Approximation Theory
    Conference paper 2020

  14. Spectral synthesis for exponentials and logarithmic length

    We study hereditary completeness of systems of exponentials on an interval such that the corresponding generating function G is small outside of a...

    Anton Baranov, Yurii Belov, Aleksei Kulikov in Israel Journal of Mathematics
    Article 11 August 2022

  17. On the zeros of lacunary-type polynomials

    Horst Alzer, Man Kam Kwong, Gradimir V. Milovanović in Optimization Letters
    Article 26 August 2020

  19. Weakly Lacunary Orthogonal Systems and Properties of the Maximal Partial Sum Operator for Subsystems

    Abstract

    For a finite orthogonal system of uniformly bounded functions, we establish the existence of sufficiently dense subsystems with the...

    B. S. Kashin, I. V. Limonova in Proceedings of the Steklov Institute of Mathematics
    Article 01 December 2020
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