منابع مشابه
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...
متن کاملSturm-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.
متن کاملSturm-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...
متن کاملRandom Sturm-Liouville operators
Selfadjoint Sturm-Liouville operators Hω on L2(a, b) with random potentials are considered and it is proven, using positivity conditions, that for almost every ω the operator Hω does not share eigenvalues with a broad family of random operators and in particular with operators generated in the same way as Hω but in L2(ã, b̃) where (ã, b̃) ⊂ (a, b).
متن کاملReflectionless Sturm-Liouville Equations
We consider compactly supported perturbations of periodic Sturm-Liouville equations. In this context, one can use the Floquet solutions of the periodic background to define scattering coefficients. We prove that if the reflection coefficient is identically zero, then the operators corresponding to the periodic and perturbed equations, respectively, are unitarily equivalent. In some appendices, ...
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ژورنال
عنوان ژورنال: The Quarterly Journal of Mathematics
سال: 1955
ISSN: 0033-5606,1464-3847
DOI: 10.1093/qmath/6.1.121