Smoothness of Wavelets

  • Aleksandr Krivoshein
  • Vladimir Protasov
  • Maria SkopinaEmail author
Part of the Industrial and Applied Mathematics book series (INAMA)


The regularity of multivariate wavelet frames with an arbitrary dilation is studied by the matrix approach. The formulas for the Hölder exponents in spaces C and \(L_p\) are obtained in terms of the joint spectral radius of the corresponding transition matrices. Some results on higher order regularity, on the local regularity, and on the asymptotics of the moduli of continuity in various spaces are presented.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2016

Authors and Affiliations

  • Aleksandr Krivoshein
    • 1
  • Vladimir Protasov
    • 2
  • Maria Skopina
    • 1
    Email author
  1. 1.Department of Applied Mathematics and Control ProcessesSaint Petersburg State UniversitySaint PetersburgRussia
  2. 2.Department of Mechanics and MathematicsLomonosov Moscow State UniversityMoscowRussia

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