The Spectral Theory of Periodic Differential Equations

a₁ absolutely continuous applied ar+1 b₁ b₂ c₁ and c₂ Chapter complex-valued conditional stability intervals constant continuous function continuously differentiable functions COROLLARY defined denote the eigenvalues differential equations differential operator Eastham eigenfunction corresponding eigenfunctions eigenvalue problems exists finite number Floquet theory Fourier coefficients Fourier series G₁(x gaps gives Hence Hilbert space Hill's equation Hochstadt instability interval integral intervals of 2.1.1 L²(EN Lemma Let p(x linear linearly independent m₁ Magnus and Winkler Math matrix non-trivial solution non-zero number of zeros obtain P₁ P₁(x P₂ P₂(x Parseval formula periodic and semi-periodic periodic problem piecewise continuous proof of Theorem proves the theorem q_(x q₁(x real number real-valued result self-adjoint self-adjoint operators semi-periodic problems solution with period solution y(x solutions of 2.1.1 spectral theory spectrum t-periodic t₁ t₂ Titchmarsh 95 values vector Winkler 67 y₁(x y₂(x Yn(x yo(x