27 citations · 52 across the 14 of their papers we have counts for
5 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…
Orthonormal dilations of Parseval wavelets
Dorin Ervin Dutkay, Deguang Han, Gabriel Picioroaga +1
We prove that any Parseval wavelet frame is the projection of an orthonormal wavelet basis for a representation of the Baumslag-Solitar group We…
Fourier series on fractals: a parallel with wavelet theory
Dorin Ervin Dutkay, Palle E. T. Jorgensen
We study orthogonality relations for Fourier frequencies and complex exponentials in Hilbert spaces with measures arising from iterated function systems (IFS). This in…
Unitary Representations of Wavelet Groups and Encoding of Iterated Function Systems in Solenoids
Dorin Ervin Dutkay, Palle E. T. Jorgensen, Gabriel Picioroaga
For points in real dimensions, we introduce a geometry for general digit sets. We introduce a positional number system where the basis for our representation is a fixed by…
Covariant representations for matrix-valued transfer operators
Dorin Ervin Dutkay, Kjetil Roysland
Motivated by the multivariate wavelet theory, and by the spectral theory of transfer operators, we construct an abstract affine structure and a multiresolution associated to a matr…