Translational averaging for completeness, characterization and oversampling of wavelets

• Autores: Richard S. Laugesen
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 53, Fasc. 3, 2002, págs. 211-250
• Idioma: inglés
• Títulos paralelos:
  • Promediado traslacional para la completitud, la caracterizacion y el sobremuestreo de ondículas
• Enlaces
  • Texto completo
• Resumen

  • The single underlying method of averaging the wavelet functional over translates yields first a new completeness criterion for orthonormal wavelet systems, and then a unified treatment of known results on characterization of wavelets on the Fourier transform side, on preservation of frame bounds by oversampling, and on equivalence of affine and quasiaffine frames. The method applies to multiwavelet systems in all dimensions, to dilation matrices that are in some cases not expanding, and to dual frame pairs.

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