Nonselfadjoint spectral problems for linear pencils \(N- \lambda P\) of ordinary differential operators with \(\lambda\)-linear boundary conditions: Completeness results

DOI10.1007/BF01191859zbMath0862.34057MaRDI QIDQ1814824

Christiane Tretter

Publication date: 2 June 1997

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

zbMATH Keywords

completeness of eigenvectorsregular boundary eigenvalue problem\(\lambda\)-dependent boundary conditions

Mathematics Subject Classification ID

General theory of ordinary differential operators (47E05) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Linear boundary value problems for ordinary differential equations (34B05) Asymptotic expansions of solutions to ordinary differential equations (34E05)

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Cites Work

• Eigenfunction expansions associated with pairs of ordinary differential expressions
• Elliptic equations in Hilbert space and associated spectral problems
• Boundary problems for ordinary differential equations with parameter in the boundary conditions
• Regular boundary value problems associated with pairs of ordinary differential expressions
• Classes of linear operators. Vol. I
• Über die Wahl der Ansatzfunktionen bei der Durchführung des Verfahrens von Galerkin
• On fundamental systems for differential equations of Kamke type
• S-hermitesche Rand-Eigenwertprobleme. I
• Zur Einordnung selbstadjungierter Rand-Eigenwertprobleme bei gewöhnlichen Differentialgleichungen in die Theorie S-hermitescher Rand-Eigenwertprobleme
• Kamke Problems. Properties of the Eigenfunctions
• On the zeros of exponential sums and integrals
• (S, S)‐adjungierte Randwertoperatoren
• AN OPERATOR GENERALIZATION OF THE LOGARITHMIC RESIDUE THEOREM AND THE THEOREM OF ROUCHÉ
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