2025/01/21 by Svetlana Jitomirskaya, Jitomirskaya, Svetlana, Wencai Liu +3 · 1 citation
Mathematics · #advanced mathematical theories #Numerical methods in inverse problems #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2501.12153
We develop tools to study arithmetically induced singular continuous spectrum in the neighborhood of the arithmetic transition in the hyperbolic regime. This leads to first transition-capturing upper bounds on packing and multifractal dimensions of spectral measures. We achieve it through the proof of partial localization of generalized eigenfunctions, another first result of its kind in the singular continuous regime. The proof is based also on a general criterion for lower bounds on concentrations of Borel measures as a corollary of boundary behavior of their Borel-type transforms, that may be of wider use and independent interest.