2010/01/25 by Dorin Ervin Dutkay, Dutkay, Dorin Ervin, Palle E. T. Jørgensen +1
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1001.4565
openalex publication_date 2010/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a family of measures μ supported in \brd and generated in the sense of Hutchinson by a finite family of affine transformations. It is known that interesting sub-families of these measures allow for an orthogonal basis in L2(μ) consisting of complex exponentials, i.e., a Fourier basis corresponding to a discrete subset Γ in \brd. Here we offer two computational devices for understanding the interplay between the possibilities for such sets Γ (spectrum) and the measures μ themselves. Our computations combine the following three tools: duality, discrete harmonic analysis, and dynamical systems based on representations of the Cuntz C^*-algebras \mathcal ON.