2011/09/21 by Dorin Ervin Dutkay, Dutkay, Dorin Ervin, Deguang Han +3
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #advanced mathematical theories #math.FA
paper · pdf · doi:10.48550/arxiv.1109.4669
openalex publication_date 2011/09/21 · arxiv created 2012/01/20 · arxiv updated 2012/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For some fractal measures it is a very difficult problem in general to prove the existence of spectrum (respectively, frame, Riesz and Bessel spectrum). In fact there are examples of extremely sparse sets that are not even Bessel spectra. In this paper we investigate this problem for general fractal measures induced by iterated function systems (IFS). We prove some existence results of spectra associated with Hadamard pairs. We also obtain some characterizations of Bessel spectrum in terms of finite matrices for affine IFS measures, and one sufficient condition of frame spectrum in the case that the affine IFS has no overlap.