A note on eigenvalues of a class of singular continuous and discrete linear Hamiltonian systems. (English) Zbl 1429.37029
The authors study the analytic and geometric
multiplicities of an eigenvalue of the following class of singular linear
Hamiltonian systems:
\[
Jy'(t)=\left(P(t)+\lambda W(t)\right)y(t),\quad t\in(a,b),
\]
where both endpoints are on the limit circle. \(W(t), P(t)\) are Hermitian matrices for any \(t\in(a,b)\) and \(W\) is nonnegative. Here \(J\) is the canonical symplectic matrix. The authors show that the two multiplicities are equal.
Reviewer: Smail Djebali (Algiers)
MSC:
| 37J06 | General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants |
| 34L15 | Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators |
| 15A18 | Eigenvalues, singular values, and eigenvectors |
| 47A75 | Eigenvalue problems for linear operators |
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