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Convergence Almost Everywhere of Orthorecursive Expansions in Functional Systems

  • Vladimir V. Galatenko
  • Taras P. Lukashenko
  • Victor A. Sadovnichiy
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 69)

Abstract

Along with the convergence in \(L^2\)-norm, convergence almost everywhere of expansions in functional systems is a property of interest for both theoretical studies and applications. In this paper we present results on convergence almost everywhere for orthorecursive expansions which are a natural generalization of classical expansions in orthogonal systems. As a corollary of a more general result, we obtain a condition on coefficients of an expansion that guarantees convergence almost everywhere. We also show that this condition cannot be relaxed.

Notes

Acknowledgments

The authors thank Dr. Alexey Galatenko for valuable comments and discussions.

The research was supported by the Russian Foundation for Basic Research (project 14–01–00417) and the President grant for the support of the leading scientific schools of the Russian Federation (grant NSh–7461.2016.1).

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Vladimir V. Galatenko
    • 1
  • Taras P. Lukashenko
    • 1
  • Victor A. Sadovnichiy
    • 1
  1. 1.Lomonosov Moscow State UniversityMoscowRussian Federation

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