2002/10/30 by Andrej Zlatoš, Andrej Zlatos, Zlatos, Andrej · 1 citation
Mathematics · Physics and Astronomy · #47A10 (Primary) 34L40 #47B39 (Secondary) #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Spectral Theory in Mathematical Physics #math-ph #math.MP #msc:34L40 #msc:47A10 #msc:47B39
paper · pdf · doi:10.48550/arxiv.math-ph/0210054
arxiv created 2002/10/30 · openalex publication_date 2002/10/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct non-random bounded discrete half-line Schr" odinger operators which have purely singular continuous spectral measures with fractional Hausdorff dimension (in some interval of energies). To do this we use suitable sparse potentials. Our results also apply to whole line operators, as well as to certain random operators. In the latter case we prove and compute an exact dimension of the spectral measures.