0000000000356886

AUTHOR

Fernando Gómez-cubillo

showing 2 related works from this author

Inner functions and local shape of orthonormal wavelets

2011

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.

Pure mathematicsHardy spacesApplied MathematicsMathematical analysisWavelet transformHardy spaceLinear subspacesymbols.namesakeGeneralized Fourier seriesWaveletOrthonormal waveletssymbolsOrthonormal basisInvariant (mathematics)OrthonormalityInner functionsMathematicsApplied and Computational Harmonic Analysis
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Evolution semigroups and time operators on Banach spaces

2010

AbstractWe present new general methods to obtain shift representation of evolution semigroups defined on Banach spaces. We introduce the notion of time operator associated with a generalized shift on a Banach space and give some conditions under which time operators can be defined on an arbitrary Banach space. We also tackle the problem of scaling of time operators and obtain a general result about the existence of time operators on Banach spaces satisfying some geometric conditions. The last part of the paper contains some examples of explicit constructions of time operators on function spaces.

Unbounded operatorMathematics::Functional AnalysisBanach spaceSchauder basisApproximation propertyNuclear operatorApplied MathematicsTime operatorFinite-rank operatorBanach manifoldOperator theoryAlgebraInterpolation spaceC0-semigroupInnovationAnalysisMathematicsMathematicsofComputing_DISCRETEMATHEMATICSJournal of Mathematical Analysis and Applications
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