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Continuous refinement equations and subdivision

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Abstract

This paper is concerned with the study of a general class of functional equations covering as special cases the relation which defines theup-function as well as equations which arise in multiresolution analysis for wavelet construction. We discuss various basic properties of solutions to these functional equations such as regularity, polynomial containment within the space spanned by their integer shifts and their computability by subdivision algorithms.

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Authors and Affiliations

  1. Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, D-5100, Aachen, Germany

    Wolfgang Dahmen

  2. IBM T.J. Watson Research Center, P.O. Box 218, 10598, Yorktown Heights, NY, USA

    Charles A. Micchelli

Authors
  1. Wolfgang Dahmen
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  2. Charles A. Micchelli
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Dahmen, W., Micchelli, C.A. Continuous refinement equations and subdivision. Adv Comput Math 1, 1–37 (1993). https://doi.org/10.1007/BF02070819

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  • DOI: https://doi.org/10.1007/BF02070819

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