6533b7dafe1ef96bd126e3c7

RESEARCH PRODUCT

Inner functions and local shape of orthonormal wavelets

Fernando Gómez-cubilloZdzislaw SuchaneckiZdzislaw Suchanecki

subject

Pure mathematicsHardy spacesApplied MathematicsMathematical analysisWavelet transformHardy spaceLinear subspacesymbols.namesakeGeneralized Fourier seriesWaveletOrthonormal waveletssymbolsOrthonormal basisInvariant (mathematics)OrthonormalityInner functionsMathematics

description

Abstract Conditions characterizing all orthonormal wavelets of L 2 ( R ) are given in terms of suitable orthonormal bases (ONBs) related with the translation and dilation operators. A particular choice of the ONBs, the so-called Haar bases, leads to new methods for constructing orthonormal wavelets from certain families of Hardy functions. Inner functions and the corresponding backward shift invariant subspaces articulate the structure of these families. The new algorithms focus on the local shape of the wavelet.

yearjournalcountryeditionlanguage
2011-05-01Applied and Computational Harmonic Analysis
10.1016/j.acha.2010.08.006http://dx.doi.org/10.1016/j.acha.2010.08.006