On the spectrum of shear flows and uniform ergodic theorems

2013/10/27 by Jonathan Ben‐Artzi, Jonathan Ben-Artzi, Ben-Artzi, Jonathan
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Stability and Controllability of Differential Equations #math.FA #math.SP

paper · pdf · doi:10.48550/arxiv.1310.7219

18 pages, no figures

arxiv created 2013/10/27 · openalex publication_date 2013/10/27 · arxiv updated 2013/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The spectra of parallel flows (that is, flows governed by first-order differential operators parallel to one direction) are investigated, on both L² spaces and weighted-L² spaces. As a consequence, an example of a flow admitting a purely singular continuous spectrum is provided. For flows admitting more regular spectra the density of states is analyzed, and spaces on which it is uniformly bounded are identified. As an application, an ergodic theorem with uniform convergence is proved.

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