Asymptotics of instability zones of Hill operators with a two term potential

DOI10.1016/j.crma.2004.06.019zbMath1063.34081OpenAlexW2024939593MaRDI QIDQ1886969

Plamen Djakov, Boris S. Mityagin

Publication date: 23 November 2004

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2004.06.019

zbMATH Keywords

Lyapunov functionSchrödinger operatorboundary value problemsHill operatorMathieu operatorinstability zoneseigenvalues of a operatorlength of spectral gaps

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) General theory of ordinary differential operators (47E05) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30)

Related Items (7)

Asymptotics of instability zones of the Hill operator with a two term potential ⋮ Divergence of spectral decompositions of Hill operators with two exponential term potentials ⋮ Refined asymptotics of the spectral gap for the Mathieu operator ⋮ On the basis property of systems of root functions of regular boundary value problems for the Sturm-Liouville operator ⋮ Multiplicities of the eigenvalues of periodic Dirac operators ⋮ Densities of short uniform random walks in higher dimensions ⋮ Simple and double eigenvalues of the Hill operator with a two-term potential

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