p-adic refinable functions and MRA-based wavelets

  • Authors:

  • A. Yu. Khrennikov;V. M. Shelkovich;M. Skopina

  • Affiliations:

  • International Center for Mathematical Modelling in Physics and Cognitive Sciences MSI, Växjö University, SE-351 95, Växjö, Sweden;Department of Mathematics, St. Petersburg State Architecture and Civil Engineering University, 2 Krasnoarmeiskaya 4, 190005, St. Petersburg, Russia;Department of Applied Mathematics and Control Processes, St. Petersburg State University,Universitetskii pr.-35, 198504 St. Petersburg, Russia

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2009

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Abstract

The main goal of this paper is the development of the MRA theory in L^2(Q"p). We described a wide class of p-adic refinement equations generating p-adic multiresolution analyses. A method for the construction of p-adic orthogonal wavelet bases within the framework of the MRA theory is suggested. A realization of this method is illustrated by an example which gives a new 3-adic wavelet basis. Another realization leads to the p-adic Haar bases which were known before.