Sturm's theorem on zeros of linear combinations of eigenfunctions

DOI10.1016/j.exmath.2018.10.002zbMath1443.34026arXiv1706.08247OpenAlexW2963352534MaRDI QIDQ1987042

Bernard Helffer, Pierre H. Bérard

Publication date: 9 April 2020

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.08247

zbMATH Keywords

Sturm-Liouville eigenvalue problemSturm's theorems

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10)

Related Items (13)

Local bifurcation and center problem for a more generalized Lorenz system ⋮ The flow of polynomial roots under differentiation ⋮ Solutions with prescribed numbers of focal points of nonoscillatory linear Hamiltonian systems ⋮ Maximization of Neumann eigenvalues ⋮ Quantitative projections in the Sturm oscillation theorem ⋮ Uncertainty Principles for Eventually Constant Sign Bandlimited Functions ⋮ Transport and Interface: An Uncertainty Principle for the Wasserstein Distance ⋮ Electrostatic interpretation of zeros of orthogonal polynomials ⋮ Indeterminacy estimates and the size of nodal sets in singular spaces ⋮ Level sets of certain Neumann eigenfunctions under deformation of Lipschitz domains application to the extended Courant property ⋮ Courant-sharp Robin eigenvalues for the square and other planar domains ⋮ On Courant’s Nodal Domain Property for Linear Combinations of Eigenfunctions Part II ⋮ Courant-sharp Robin eigenvalues for the square: The case of negative Robin parameter

Cites Work

• Topological properties of eigenoscillations in mathematical physics
• Sturm and Liouville's work on ordinary linear differential equations. The emergence of Sturm-Liouville theory
• Oscillation of Fourier integrals with a spectral gap.
• On Courant's nodal domain property for linear combinations of eigenfunctions. I
• Quantitative projections in the Sturm oscillation theorem
• On delusive nodal sets of free oscillations
• Remarks on courant's nodal line theorem
• The Courant‐Herrmann conjecture
• Sturm's theorem on the zeros of sums of eigenfunctions: Gelfand's strategy implemented
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