A Characterization of Nonuniform Multiwavelets Using Dimension Function

Abstract

In this article, we present a characterization of nonuniform multiwavelets associated to a nonuniform multiresolution analysis (NUMRA) having finite multiplicity in terms of its dimension function. This, in turn, improves the main result of Gabardo and Yu given in (J Math Anal Appl 323(2):798–817, 2006). The concept of NUMRA was introduced by Gabardo and Nashed in which the translation set is a spectrum that is no longer a group.

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Correspondence to Shiva Mittal.

Additional information

The first author is supported by Libyan government for pursuing her Ph.D. thesis at SHIATS, Deemed to be University, Allahabad, India.

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Atlouba, N.A.S., Mittal, S. & Shukla, N.K. A Characterization of Nonuniform Multiwavelets Using Dimension Function. Results Math 72, 1239–1255 (2017). https://doi.org/10.1007/s00025-016-0648-2

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Keywords

  • MRA with multiplicity D
  • NUMRA
  • spectral pairs
  • multiwavelets
  • multiscaling functions
  • dimension function

Mathematics Subject Classification

  • 42C40
  • 65T60