144 citations · 1.1k across the 203 of their papers we have counts for
19 papers · 1 filter
Quasiperiodic Spectra and Orthogonality for Iterated Function System Measures
Dorin Ervin Dutkay, Palle E. T. Jorgensen
We extend classical basis constructions from Fourier analysis to attractors for affine iterated function systems (IFSs). This is of interest since these attractors have fractal fea…
Analysis of orthogonality and of orbits in affine iterated function systems
Dorin Ervin Dutkay, Palle E. T. Jorgensen
We introduce a duality for Affine Iterated Function Systems (AIFS) which is naturally motivated by group duality in the context of traditional harmonic analysis. Our affine systems…
Frame analysis and approximation in reproducing kernel Hilbert spaces
Palle E. T. Jorgensen
We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbe…
Localized bases in L^2(0,1) and their use in the analysis of Brownian motion
Palle E. T. Jorgensen, Anilesh Mohari
Motivated by problems on Brownian motion, we introduce a recursive scheme for a basis construction in the Hilbert space L^2(0,1) which is analogous to that of Haar and Walsh. More…
Sample Paths in Wavelet Theory
Palle E. T. Jorgensen
We consider a class of convergence questions for infinite products that arise in wavelet theory when the wavelet filters are more singular than is traditionally built into the assu…
A non-MRA frame wavelet with rapid decay
Lawrence Baggett, Palle Jorgensen, Kathy Merrill +1
A generalized filter construction is used to build an example of a non-MRA normalized tight frame wavelet for dilation by 2 in . This example has the same multiplic…