# Wavelets on fractals.

Dorin E. Dutkay; Palle E.T. Jorgensen

Revista Matemática Iberoamericana (2006)

- Volume: 22, Issue: 1, page 131-180
- ISSN: 0213-2230

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topDutkay, 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 < s < 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 < s < 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 -

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