S. Pedersen

activity

19992002

collaborators

6 papers

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 $D$ be a bounded domain in $R^{n}$ whose boundary has a Minkowski dimension $α < n$ . Suppose that $E_{Λ} = {e^{2 π i x \cdot λ}}_{λ \in Λ}$ , $Λ$ 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…

math.SP2000

Commuting self-adjoint extensions of symmetric operators defined from the partial derivatives

Palle E. T. Jorgensen, Steen Pedersen

We consider the problem of finding commuting self-adjoint extensions of the partial derivatives {(1/i)(\partial/\partial x_j):j=1,...,d} with domain C_c^\infty(Ω) where the self-ad…

math.FA1999

Orthogonal harmonic analysis and scaling of fractal measures

Palle E. T. Jorgensen, Steen Pedersen

We show that certain iteration systems lead to fractal measures admitting exact orthogonal harmonic analysis.

math.FA1999

Spectral pairs in Cartesian coordinates

Palle E. T. Jorgensen, Steen Pedersen

Let $Ω \subset R^{d}$ have finite positive Lebesgue measure, and let $L^{2} (Ω)$ be the corresponding Hilbert space of $L^{2}$ -functions on $Ω$ . We shall con…