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Smoothness of Wavelets

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Multivariate Wavelet Frames

Part of the book series: Industrial and Applied Mathematics ((INAMA))

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Abstract

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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Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Control Processes, Saint Petersburg State University, Universitetsky prospekt 35, Saint Petersburg, Russia

    Aleksandr Krivoshein & Maria Skopina

  2. Department of Mechanics and Mathematics, Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow, Russia

    Vladimir Protasov

Authors
  1. Aleksandr Krivoshein
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  2. Vladimir Protasov
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  3. Maria Skopina
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Corresponding author

Correspondence to Maria Skopina .

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© 2016 Springer Nature Singapore Pte Ltd.

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Krivoshein, A., Protasov, V., Skopina, M. (2016). Smoothness of Wavelets. In: Multivariate Wavelet Frames. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-10-3205-9_6

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