Eigenvalue estimates and trace formulas for the matrix Hill's equation

DOI10.1006/jdeq.2000.3785zbMath0968.34070OpenAlexW2084953816MaRDI QIDQ1585989

R. Smith

Publication date: 16 September 2001

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.2000.3785

zbMATH Keywords

asymptotic expansiontrace formulaperiodic eigenvaluesmatrix Hill equation

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items (15)

Trace formula for the matrix Sturm-Liouville operator ⋮ Time-dependent high-contrast subwavelength resonators ⋮ A third order operator with periodic coefficients on the real line ⋮ Trace formulae for the matrix Schrödinger equation with energy-dependent potential ⋮ Estimates of large eigenvalues and trace formula for the vectorial Sturm-Liouville equations ⋮ Conformal spectral theory for the monodromy matrix ⋮ On a fundamental system of solutions of the matrix Schrödinger equation with a polynomial energy-dependent potential ⋮ A spectral transform for the matrix Hill's equation ⋮ An inverse spectral problem for the matrix Sturm-Liouville operator on the half-line ⋮ The Lyapunov function for Schrödinger operators with a periodic \(2\times 2\) matrix potential ⋮ Spectral asymptotics for the third order operator with periodic coefficients ⋮ The periodic Euler-Bernoulli equation ⋮ Spectral estimates for a periodic fourth-order operator ⋮ Trace formula and inverse nodal problem for a conformable fractional Sturm-Liouville problem ⋮ An inverse problem for the matrix Schrödinger equation

Cites Work

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• Sturm-Liouville operators and applications. Transl. from the Russian by A. Iacob
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• Eigenvalue and eigenfunction asymptotics for regular Sturm-Liouville problems
• The \(\xi\) function
• Perturbation theory for linear operators.
• A trace formula for multidimensional Schrödinger operators
• Trace formulas for Sturm-Liouville differential operators
• The inverse problem for periodic potentials
• Trace formulas for the schroedinger operator
• Trace Formulas and the Behaviour of Large Eigenvalues
• Compactness of Floquet isospectral sets for the matrix Hill's equation
• Large Eigenvalues and Trace Formulas for Matrix Sturm--Liouville Problems
• On the Determinant of Elliptic Boundary Value Problems on a Line Segment

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