Wavelets on fractals

• Autores: Palle E. T. Jorgensen, Dorin Ervin Dutkay
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 22, Nº 1, 2006, págs. 131-180
• Idioma: inglés
• DOI: 10.4171/rmi/452
• Títulos paralelos:
  • Ondículas sobre fractales
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• Resumen

  • We show that there are Hilbert spaces constructed from the Hausdorff measures Hs on the real line R with 0 < s < 1 which admit multiresolution wavelets. For the case of the middle-third Cantor set C Ì [0,1], the Hilbert space is a separable subspace of L2(R, (dx)s) where s = log3(2). While we develop the general theory of multiresolutions in fractal Hilbert spaces, the emphasis is on the case of scale 3 which covers the traditional Cantor set C.