71 citations · 326 across the 43 of their papers we have counts for
6 papers · 1 filter
Kadison-Singer from mathematical physics: An introduction
Palle E. T. Jorgensen
We give an informal overview of the Kadison-Singer extension problem with emphasis on its initial connections to Dirac's formulation of quantum mechanics. Let H be an infinite dime…
Some recent trends from research mathematics and their connections to teaching: Case studies inspired by parallel developments in science and technology
Palle E. T. Jorgensen
We will outline our ideas for teaching in the core mathematics disciplines. They are based on our own experience in teaching at a number of universities in the USA, as well as in E…
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…
Harmonic Analysis of Fractal Measures
Palle E. T. Jorgensen, Steen Pedersen
This paper introduces Fourier duality for a class of affine iterated function systems (IFS) T_i. These systems are determined by a finite family of contractive affine maps in R^d.…
Fourier frequencies in affine iterated function systems
Dorin E. Dutkay, Palle E. T. Jorgensen
We examine two questions regarding Fourier frequencies for a class of iterated function systems (IFS). These are iteration limits arising from a fixed finite families of affine and…
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…