J. Reine und Angew. Math. 736, 285-315 (2018) [DOI: 10.1515/crelle-2015-0034]

Spectral asymptotics for canonical systems

Jonathan Eckhardt, Aleksey Kostenko, and Gerald Teschl

Based on continuity properties of the de Branges correspondence, we develop a new approach to study the high-energy behavior of Weyl-Titchmarsh and spectral functions of 2×2 first order canonical systems. Our results improve several classical results and solve open problems posed by previous authors. Furthermore, they are applied to radial Dirac and radial Schrödinger operators as well as to Krein strings and generalized indefinite strings.

MSC2010: Primary 34B20, 47B15; Secondary 47B32, 34B30
Keywords: Canonical systems, spectral asymptotics, Weyl-Titchmarsh function

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