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p-Adic wavelets and their applications

  • S. V. KozyrevEmail author
  • A. Yu. Khrennikov
  • V. M. Shelkovich
Article

Abstract

The theory of p-adic wavelets is presented. One-dimensional and multidimensional wavelet bases and their relation to the spectral theory of pseudodifferential operators are discussed. For the first time, bases of compactly supported eigenvectors for p-adic pseudodifferential operators were considered by V.S. Vladimirov. In contrast to real wavelets, p-adic wavelets are related to the group representation theory; namely, the frames of p-adic wavelets are the orbits of p-adic transformation groups (systems of coherent states). A p-adic multiresolution analysis is considered and is shown to be a particular case of the construction of a p-adic wavelet frame as an orbit of the action of the affine group.

Keywords

Coherent State STEKLOV Institute Wavelet Function Wavelet Base Wavelet Frame 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  • S. V. Kozyrev
    • 1
    Email author
  • A. Yu. Khrennikov
    • 2
  • V. M. Shelkovich
    • 3
    • 4
  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia
  2. 2.International Center for Mathematical Modeling in Physics, Engineering and Cognitive SciencesLinnaeus UniversityVäxjöSweden
  3. 3.Saint-Petersburg State University of Architecture and Civil EngineeringSt. PetersburgRussia
  4. 4.Department of Higher Mathematics and Mathematical Physics, Faculty of PhysicsSt. Petersburg State UniversitySt. PetersburgRussia

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