Along the lines of Atkinson [3], a spectral theorem is proved for the boundary value problem {Jz' + f(t)Jz + P(t)z = lambda B(t)z x(0) = x(T) = 0, t is an element of [0,T], z = (x, y) is an element of R-N x R-N, where f(t) is real-valued and P(t), B(t) are symmetric matrices, with B(t) positive definite. A suitable rotation index associated to the system is used to highlight the connections between the eigenvalues and the nodal properties of the corresponding eigenfunctions.
A note on a linear spectral theorem for a class of first order systems in $mathbb{R}^{2N}$
BOSCAGGIN, Alberto;
2010-01-01
Abstract
Along the lines of Atkinson [3], a spectral theorem is proved for the boundary value problem {Jz' + f(t)Jz + P(t)z = lambda B(t)z x(0) = x(T) = 0, t is an element of [0,T], z = (x, y) is an element of R-N x R-N, where f(t) is real-valued and P(t), B(t) are symmetric matrices, with B(t) positive definite. A suitable rotation index associated to the system is used to highlight the connections between the eigenvalues and the nodal properties of the corresponding eigenfunctions.
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