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Convergence Almost Everywhere of Orthorecursive Expansions in Systems of Translates and Dilates

  • Vladimir V. Galatenko
  • Taras P. Lukashenko
  • Victor A. Sadovnichiy
Chapter
Part of the Understanding Complex Systems book series (UCS)

Abstract

Systems of translates and dilates have been widely studied in the last decades. In particular, V.I. Filippov and P. Oswald obtained conditions on a generating function which guarantee that dyadic translates and dilates of this function form a representation system in Lp[0, 1]. A.Yu. Kudryavtsev and A.V. Politov showed that under a slightly harder condition on a generating function each element f ∈ L2[0, 1] is represented by its orthorecursive expansion in this system. Here we continue studying orthorecursive expansions in systems of dyadic translates and dilates and present results on convergence almost everywhere of these expansions.

Notes

Acknowledgements

The authors thank Dr. Alexey Galatenko for valuable comments and discussions. The research was supported by the Russian Federation Government Grant No. 14.W03.31.0031.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

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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