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IMA Journal of Applied Mathematics Advance Access published online on October 11, 2009
IMA Journal of Applied Mathematics, doi:10.1093/imamat/hxp027
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© The Author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Construction of orthogonal multi-wavelets using generalized-affine fractal interpolation functions

P. Bouboulis{dagger}

Department of Informatics and Telecommunications, Telecommunications and Signal Processing, University of Athens, Panepistimiopolis 157 84, Athens, Greece

{dagger} Email: bouboulis{at}di.uoa.gr

Received on May 14, 2008; Revision received June 18, 2009. Accepted on August 27, 2009

We present a new construction of fractal interpolation surfaces defined on arbitrary rectangular lattices. We use this construction to form finite sets of fractal interpolation functions (FIFs) that generate multiresolution analyses of L2(R2) of multiplicity r. These multiresolution analyses are based on the dilation properties of the construction. The associated multi-wavelets are orthogonal and discontinuous functions. We give concrete examples to illustrate the method and generalize it to form multiresolution analyses of L2(Rd), d > 2. To this end, we prove some results concerning the Hölder exponent of FIFs defined on [0, 1]d.

Keywords: fractal interpolation functions; fractal interpolation surfaces; fractals; moments; Hölder; multi-wavelets.


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