Estimates of large eigenvalues and trace formula for the vectorial Sturm-Liouville equations

DOI10.1216/RMJ-2013-43-6-2049zbMath1292.34082OpenAlexW2031229494MaRDI QIDQ2439543

Chuan-Fu Yang, Zhen-you Huang, Xiao-Ping Yang

Publication date: 14 March 2014

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1393336669

zbMATH Keywords

eigenvalue asymptoticsinverse spectral problemtrace formulavectorial Sturm-Liouville problem

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) General spectral theory of ordinary differential operators (34L05) General theory of ordinary differential operators (47E05) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Inverse problems involving ordinary differential equations (34A55) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Cites Work

• Gaps and bands of one dimensional periodic Schrödinger operators
• A generalization of the trace concept
• Sturm-Liouville operators and applications. Transl. from the Russian by A. Iacob
• The spectrum of Hill's equation
• Eigenvalue and eigenfunction asymptotics for regular Sturm-Liouville problems
• The \(\xi\) function
• Isospectral vector-valued Sturm-Liouville problems
• Borg-type theorems for matrix-valued Schrödinger operators
• Eigenvalue estimates and trace formulas for the matrix Hill's equation
• The multiplicity of spectra of a vectorial Sturm-Liouville differential equation of dimension two and some applications
• Discrete and continuous boundary problems
• Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte
• Weyl-Titchmarsh M -Function Asymptotics for Matrix-valued Schrödinger Operators
• On the n -dimensional Ambarzumyan's theorem
• Asymptotic estimates for the Sturm-Liouville spectrum
• On an extension of the theorem of V. A. Ambarzumyan
• The inverse problem for periodic potentials
• Trace Formulas and the Behaviour of Large Eigenvalues
• Weyl–Titchmarsh $M$-Function Asymptotics, Local Uniqueness Results, Trace Formulas, and Borg-type Theorems for Dirac Operators
• Large Eigenvalues and Trace Formulas for Matrix Sturm--Liouville Problems
• Isospectral sets and inverse problems for vector-valued Sturm–Liouville equations
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