On algebraic multiplicity of (anti)periodic eigenvalues of Hill’s equations
Copyright policy )On algebraic multiplicity of (anti)periodic eigenvalues of Hill’s equations
We construct two explicit examples of Hill’s equations with complex-valued potentials such that the algebraic multiplicity of some (anti)periodic eigenvalue E E equals 1 + 2 p i 1+2p_{i} with p i ≥ 1 p_{i}\geq 1 , where p i p_{i} denotes the immovable part of E E as a Dirichlet eigenvalue. These examples confirm a phenomena about Hill’s equations in (Gesztesy and Weikard, Acta Math. 176 (1996), 73–107).
- Tsinghua University China (People's Republic of)
- National Taiwan University of Arts Taiwan
Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators, Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators, Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
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