Wavelets on fractals.

Dutkay, Dorin E., and Jorgensen, Palle E.T.. "Wavelets on fractals.." Revista Matemática Iberoamericana 22.1 (2006): 131-180. <http://eudml.org/doc/41968>.

@article{Dutkay2006,
abstract = {We show that there are Hilbert spaces constructed from the Hausdorff measures Hs on the real line R with 0 &lt; s &lt; 1 which admit multiresolution wavelets. For the case of the middle-third Cantor set C ⊂ [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.},
author = {Dutkay, Dorin E., Jorgensen, Palle E.T.},
journal = {Revista Matemática Iberoamericana},
keywords = {Ondículas; Espacios de Hilbert; Distancia de Hausdorff; Conjuntos de Cantor; Sistemas de funciones iteradas; Fractales; iterated function systems (IFS); fractal; wavelets; unitary operators; orthonormal basis (ONB); spectrum; transfer operator; cascade approximation; scaling; translation; Hilbert spaces; Hausdorff measures; Cantor set},
language = {eng},
number = {1},
pages = {131-180},
title = {Wavelets on fractals.},
url = {http://eudml.org/doc/41968},
volume = {22},
year = {2006},
}

TY - JOUR
AU - Dutkay, Dorin E.
AU - Jorgensen, Palle E.T.
TI - Wavelets on fractals.
JO - Revista Matemática Iberoamericana
PY - 2006
VL - 22
IS - 1
SP - 131
EP - 180
AB - We show that there are Hilbert spaces constructed from the Hausdorff measures Hs on the real line R with 0 &lt; s &lt; 1 which admit multiresolution wavelets. For the case of the middle-third Cantor set C ⊂ [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.
LA - eng
KW - Ondículas; Espacios de Hilbert; Distancia de Hausdorff; Conjuntos de Cantor; Sistemas de funciones iteradas; Fractales; iterated function systems (IFS); fractal; wavelets; unitary operators; orthonormal basis (ONB); spectrum; transfer operator; cascade approximation; scaling; translation; Hilbert spaces; Hausdorff measures; Cantor set
UR - http://eudml.org/doc/41968
ER -