Relative Eigenvalue Problems for Ordinary Differential Operators |
Common terms and phrases
A¯¹B allowable coefficient analytic assume assumptions boundary conditions bounded on L2 bounded operator Chapter closure compact operator conditions f(0 constant continuously embedded defined denote dense differential operators domain eigenfunction eigenvalues equivalent finite sums follows formal operator Fredholm operators G₁f G₂ G₂f H₁ hence Hilbert space implies inner product integer interpolation last section Lemma Lemma 15 Lemma 9 Let A,B Let f linear combination linearly independent m₁ m₂ matrix non-zero eigenvalues norm null space one-to-one operator on L2 order at least P₁ pair A,B perturbation projection associated Proof R(EN R(P² R₂ range requirements satisfies the hypotheses scalar self-adjoint seminorm separated boundary conditions sequence set of boundary simple pole spectral and complete subspace of H super-regular suppose theory topology vector zeros of M(u Σ Σ