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math.CA2002
Estimates on the Spectrum of Fractals Arising From Affine Iterations
Palle E. T. Jorgensen, Steen Pedersen
In the first section we review recent results on the harmonic analysis of fractals generated by iterated function systems with emphasis on spectral duality. Classical harmonic anal…
math.CA2001
How large are the spectral gaps?
Alex Iosevich, Steen Pedersen
Let be a bounded domain in whose boundary has a Minkowski dimension . Suppose that , an infinite discrete subset o…
math.CA2001
Fourier bases and a distance problem of Erd\H os
Alex Iosevich, Nets Katz, Steen Pedersen
We prove that no ball admits a non-harmonic orthogonal basis of exponentials. We use a combinatorial result, originally studied by Erd\H os, which says that the number of distances…