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Quincunx multiresolution analysis for L 2(ℚ 22 )

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Abstract

With an eye on applications in quantum mechanics and other areas of science, much work has been done to generalize traditional analytic methods to p-adic systems. In 2002 the first paper on p-adic wavelets was published. Since then p-adic wavelet sets, multiresolution analyses, and wavelet frames have all been introduced. However, so far all constructions have involved dilations by p. This paper presents the first construction of a p-adic wavelet system with a more general matrix dilation, laying the foundation for further work in this direction.

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Authors and Affiliations

  1. Laboratory for Integrative and Medical Biophysics, National Institute for Child Health and Human Development, National Institutes of Health, 9 Memorial Dr. Bethesda, Bethesda, MD, 20892, USA

    Emily J. King

  2. Department of Applied Mathematics and Control Processes, St. Petersburg State University, Universitetskii pr. 35, 198504, St.Petersburg, Russia

    Maria A. Skopina

Authors
  1. Emily J. King
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  2. Maria A. Skopina
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Correspondence to Emily J. King.

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The text was submitted by the authors in English.

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King, E.J., Skopina, M.A. Quincunx multiresolution analysis for L 2(ℚ 22 ). P-Adic Num Ultrametr Anal Appl 2, 222–231 (2010). https://doi.org/10.1134/S2070046610030040

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  • DOI: https://doi.org/10.1134/S2070046610030040

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