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Lattice and continuum wavelets and the block renormalization group

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Abstract

We obtain a resolution of the identity operator, for functions on a latticeɛZ d, which is derived from the block renormalization group. We use eigenfunctions of the terms of the decomposition to form a basis forl 2(ɛZd) and show how the basis is generated from lattice wavelets. The lattice spacingɛ is taken to zero and continuum wavelets are obtained.

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Authors and Affiliations

  1. Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, 30.270, Belo Horizonte, Brazil

    Michael O'Carroll

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  1. Michael O'Carroll
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O'Carroll, M. Lattice and continuum wavelets and the block renormalization group. J Stat Phys 71, 415–423 (1993). https://doi.org/10.1007/BF01058429

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  • DOI: https://doi.org/10.1007/BF01058429

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