Search results for "Generalized Fourier series"

showing 2 items of 2 documents

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
researchProduct

Wavelet-like orthonormal bases for the lowest Landau level

1994

As a first step in the description of a two-dimensional electron gas in a magnetic field, such as encountered in the fractional quantum Hall effect, we discuss a general procedure for constructing an orthonormal basis for the lowest Landau level, starting from an arbitrary orthonormal basis in L2(R). We discuss in detail two relevant examples coming from wavelet analysis, the Haar and the Littlewood-Paley bases.

PhysicsMathematics::Functional AnalysisGeneral Physics and AstronomyStatistical and Nonlinear PhysicsLandau quantizationMagnetic fieldGeneralized Fourier seriesWaveletFractional quantum Hall effectOrthonormal basisQuantum field theorySettore MAT/07 - Fisica MatematicaMutually unbiased basesMathematical PhysicsMathematical physics
researchProduct