Eigenstructure of nonselfadjoint complex discrete vector Sturm-Liouville problems.
Eigensystem of an L 2-perturbed harmonic oscillator is an unconditional basis
For any complex valued L p-function b(x), 2 ≤ p < ∞, or L ∞-function with the norm ‖b↾L ∞‖ < 1, the spectrum of a perturbed harmonic oscillator operator L = −d 2/dx 2 + x 2 + b(x) in L 2(ℝ1) is discrete and eventually simple. Its SEAF (system of eigen- and associated functions) is an unconditional basis in L 2(ℝ).
Équilibre instable en régime semi-classique
Estimates for Derivatives and Integrals of Eigenfunctions and Associated Functions of Nonselfadjoint Sturm-Liouville Operator With Discontinuous Coefficients (II)