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).

We prove an explicit formula for the spectral expansions in L(R) generated by selfadjoint differential operators (−1) d dx2n + n−1

For selfadjoint elliptic operators in divergence form with ?-periodic coefficients of even order 2m ? 4 we approximate the resolvent energy operator norm $$ {\left\Vert \bullet \right\Vert}_{L^2\to {H}^m} a remainder ?2 as ? ? 0.

We prove a general operator theoretic result that asserts that many multiplicity two selfadjoint operators have simple singular spectrum. © 2005 Elsevier Inc. All rights reserved.

Let H be a Hilbert space, L(H) the algebra of all bounded linear operators on H and 〈 , 〉A : H×H → C the bounded sesquilinear form induced by a selfadjoint A ∈ L(H), 〈ξ, η〉A = 〈Aξ, η〉, ξ, η ∈ H. Given T ∈ L(H), T is A-selfadjoint if AT = T ∗A. If S ⊆ H is a closed subspace, we study the set of A-selfadjoint projections onto S, P(A,S) = {Q ∈ L(H) : Q = Q , R(Q) = S , AQ = Q∗A} for different choi...

We characterize the essentially normal composition operators induced on the Hardy space H2 by linear fractional maps; they are either compact, normal, or (the nontrivial case) induced by parabolic non-automorphisms. These parabolic maps induce the first known examples of nontrivially essentially normal composition operators. In addition we characterize those linearfractionally induced compositi...