The asymptotic form of the spectral functions associated with a class of Sturm–Liouville equations

DOI10.1017/S030821050001386XzbMath0577.34015MaRDI QIDQ3699166

B. J. Harris

Publication date: 1985

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

spectral functionsStieltjes inversion formulaTitchmarsh-Weyl m-functions

Mathematics Subject Classification ID

Ordinary differential operators (34L99)

Related Items (12)

The asymptotic form of the Titchmarsh-Weyl m-function for second-order linear differential equations with analytic coefficients ⋮ Asymptotics of the Titchmarsh—Weyl m-coefficient for non-integrable potentials ⋮ The asymptotic nature of spectral functions in Sturm-Liouville problems with continuous spectrum ⋮ The form of the spectral functions associated with a class of Sturm–Liouville equations with integrable coefficient ⋮ The form of the spectral functions associated with Sturm‐Liouville problems with continuous spectrum ⋮ Asymptotic behavior of the density of the spectral measure of the Sturm-Liouville singular operator ⋮ An inverse problem involving the Titchmarsh–Weyl m-function ⋮ The asymptotic form of the spectral function in Sturm–Liouville problems with a large potential like −x^c(c ≦ 2) ⋮ Asymptotic behavior of the spectral measure density of a singular Sturm-Liouville operator as \(\lambda \rightarrow -\infty\) ⋮ The form of the spectral functions associated with Sturm-Liouville equations with large negative potential ⋮ The asymptotic form of the Titchmarsh–Weyl m-function associated with a second order differential equation with locally integrable coefficient ⋮ A property of the asymptotic series for a class of Titchmarsh–Weyl m-functions

Cites Work

• Criteria for Sturm-Liouville equations to have continuous spectra
• On Titchmarsh-Weyl \(M(\lambda)\)-functions for linear Hamiltonian system
• Bounds for the Point Spectra of Sturm-Liouville Equations
• On the Titchmarsh–Weyl m -function
• On the location of the Weyl circles
• A return to the Hardy-Littlewood integral inequality
• The Asymptotic Form of the Titchmarsh-Weyl Coefficient for Dirac Systems
• On a Class of Integral Inequalities
• On the asymptotic form of the Titchmarsh-Weylm-coefficient†
• On a Property of the M -Coefficient of a Secondorder Linear Differential Equation

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