Asymptotic behavior of spectral measures of Krein's and Kotani's strings

DOI10.1215/0023608X-2010-007zbMath1206.34107OpenAlexW1973572422MaRDI QIDQ1958476

Shinzo Watanabe, Yuji Kasahara

Publication date: 29 September 2010

Published in: Kyoto Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/0023608x-2010-007

zbMATH Keywords

second-order differential operatorspectral measureStieltjes transformsHerglotz functionKrein's stringKotani's strig

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) General spectral theory of ordinary differential operators (34L05) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20)

Related Items (7)

Krein's strings whose spectral functions are of polynomial growth ⋮ Limit behavior of Weyl coefficients ⋮ Harmonic extension technique for non-symmetric operators with completely monotone kernels ⋮ Diffusions with Bessel-like drifts ⋮ Spectral asymptotics for canonical systems ⋮ Asymptotic behavior of the transition density of an ergodic linear diffusion ⋮ Tauberian theorem for harmonic mean of Stieltjes transforms and its applications to linear diffusions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Krein's strings with singular left boundary
• Remarks on Krein-Kotani's correspondence between strings and Herglotz functions
• A density formula for the law of time spent on the positive side of one-dimensional diffusion processes
• On time inversion of one-dimensional diffusion processes

This page was built for publication: Asymptotic behavior of spectral measures of Krein's and Kotani's strings