On a necessary aspect for the Riesz basis property for indefinite Sturm-Liouville problems

DOI10.1002/mana.201300104zbMath1311.34056arXiv1202.2444OpenAlexW1568240680WikidataQ62469516 ScholiaQ62469516MaRDI QIDQ2929430

Aleksey S. Kostenko

Publication date: 12 November 2014

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.2444

zbMATH Keywords

Riesz basisindefinite Sturm-Liouville problemHELP inequalityLRG condition

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Weyl theory and its generalizations for ordinary differential equations (34B20) Eigenvalue problems for linear operators (47A75) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (4)

The Critical Point Infinity Associated with Indefinite Sturm–Liouville Problems ⋮ Indefinite Sturm-Liouville operators in polar form ⋮ The similarity problem for indefinite Sturm-Liouville operators and the HELP inequality ⋮ The Riesz basis property of an indefinite Sturm-Liouville problem with non-separated boundary conditions

Cites Work

• Some properties of eigenfunctions of linear pencils
• Indefinite Sturm-Liouville problems and half-range completeness
• The similarity problem for \(J\)-nonnegative Sturm-Liouville operators
• The similarity problem for indefinite Sturm-Liouville operators and the HELP inequality
• The Riesz basis property of an indefinite Sturm-Liouville problem with non-separated boundary conditions
• The similarity problem for indefinite Sturm-Liouville operators with periodic coefficients
• A review of a Riesz basis property for indefinite Sturm-Liouville problems
• Indefinite Sturm–Liouville operators with the singular critical point zero
• A general version of the Hardy–Littlewood–Polya–Everitt (HELP) inequality
• A return to the Hardy-Littlewood integral inequality
• 𝑅-functions—analytic functions mapping the upper halfplane into itself
• Norm inequalities involving derivatives
• Sturm–Liouville problems with indefinite weights and Everitt's inequality
• Spectral Asymptotics for Sturm-Liouville Equations
• Indefinite Sturm-Liouville operators (sgn x)(-d2/dx2+q(x)) with finite-zone potentials
• HELP inequalities for limit-circle and regular problems
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