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Quincunx multiresolution analysis for L 2(ℚ 2 2 )

Research Articles

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.

Key words

p-adic MRA quincunx matrix wavelet basis 

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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Laboratory for Integrative and Medical Biophysics, National Institute for Child Health and Human DevelopmentNational Institutes of HealthBethesdaUSA
  2. 2.Department of Applied Mathematics and Control ProcessesSt. Petersburg State UniversitySt.PetersburgRussia

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