Symmetry in nonselfadjoint Sturm-Liouville systems

The Determinant Method for Nonselfadjoint Singular Sturm - Liouville Problems

We are concerned with the computation of eigenvalues of singular nonselfadjoint Sturm — Liouville problems by the method of determinants. The representation of a differential operator by an infinite matrix allows the use of Lidskii’s theorem to define its determinant. The finite section is then used to compute eigenvalues in a simple way. This direct method borrows stable methods from numerical...

Eigenstructure of Nonselfadjoint Complex Discrete Vector Sturm-liouville Problems

Sturm - Liouville Systems Are Riesz - Spectral Systems

where x, u and y are the system state, input and output, respectively, A is a densely defined differential linear operator on an (infinite-dimensional) Hilbert space (e.g., L(a, b), a, b ∈ R), which generates a C0-semigroup, and B, C and D are bounded linear operators. Moreover, if A is a Riesz-spectral operator, it possesses several interesting properties, regarding in particular observability...

Sturm-liouville Problems

Regular and singular Sturm-Liouville problems (SLP) are studied including the continuous and differentiable dependence of eigenvalues on the problem. Also initial value problems (IVP) are considered for the SL equation and for general first order systems.

Sturm-liouville Eigenvalue Characterizations

We study the relationship between the eigenvalues of separated self-adjoint boundary conditions and coupled self-adjoint conditions. Given an arbitrary real coupled boundary condition determined by a coupling matrix K we construct a one parameter family of separated conditions and show that all the eigenvalues for K and −K are extrema of the eigencurves of this family. This characterization mak...