27 citations · 52 across the 14 of their papers we have counts for
7 papers · 1 filter
Duality questions for operators, spectrum and measures
Dorim Ervin Dutkay, Palle E. T. Jorgensen
We explore spectral duality in the context of measures in $\br^n$, starting with partial differential operators and Fuglede's question (1974) about the relationship between orthogo…
Probability and Fourier duality for affine iterated function systems
Dorin Ervin Dutkay, Palle Jorgensen
Let be a positive integer, and let be a finite measure on $\br^d$. In this paper we ask when it is possible to find a subset in $\br^d$ such that the corresponding comp…
Parseval frames for ICC groups
Dorin Ervin Dutkay, Deguang Han, Gabriel Picioroaga
We analyze Parseval frames generated by the action of an ICC group on a Hilbert space. We parametrize the set of all such Parseval frames by operators in the commutant of the corre…
On the spectra of a Cantor measure
Dorin Ervin Dutkay, Deguang Han, Qiyu Sun
We analyze all orthonormal bases of exponentials on the Cantor set defined by Jorgensen and Pedersen in J. Anal. Math. 75,1998, pp 185-228. A complete characterization for all maxi…
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…