In this paper, we develop certain aspects of perturbation theory for self-adjoint operators subject to small variations their domains. We use the abstract boundary triplets quantify such perturbations and give second-order asymptotic analysis resolvents, spectral projections, discrete eigenvalues corresponding operators. particular, derive explicit formulas first variation Hessian eigenvalue cu...

We investigate the asymptotic behaviour of large eigenvalues for a class of finite difference self-adjoint operators with compact resolvent in l2.

We prove explicitly that to every discrete, semibounded Hamiltonian with constant degeneracy and with finite sum of the squares of the reciprocal of its eigenvalues and whose eigenvectors span the entire Hilbert space there exists a characteristic self-adjoint time operator which is canonically conjugate to the Hamiltonian in a dense subspace of the Hilbert space. Moreover, we show that each ch...

LetA be a ν-vector of self-adjoint, pairwise commuting operators andB a bounded operator of classCn0 (A). We prove a Taylor-like expansion of the commutator [B, f(A)] for a large class of functions f : Rν → R, generalising the one-dimensional result where A is just a self-adjoint operator. This is done using almost analytic extensions and the higher-dimensional Helffer-Sjöstrand formula.

In this paper we consider the problem of the existence of higher derivatives of the function t → ϕ(A + tK), where ϕ is a function on the real line, A is a self-adjoint operator, and K is a bounded self-adjoint operator. We improve earlier results by Sten'kin. In order to do this, we give a new approach to multiple operator integrals. This approach improves the earlier approach given by Sten'kin...

The spectral shift function for a trace class perturbation of a self-adjoint (unitary) operator plays a very important role in perturbation theory. It was introduced in a special case by I.M. Lifshitz [L] and in the general case by M.G. Krein [Kr1]. He showed that for a pair of self-adjoint (not necessarily bounded) operators A and B satisfying B −A ∈ S1 there exists a unique function ξ ∈ L 1(R...

We prove explicitly that to every discrete, semibounded Hamiltonian with constant degeneracy and with finite sum of the squares of the reciprocal of its eigenvalues and whose eigenvectors span the entire Hilbert space there exists a characteristic self-adjoint time operator which is canonically conjugate to the Hamiltonian in a dense subspace of the Hilbert space. Moreover, we show that each ch...

Abstract We improve known perturbation results for self-adjoint operators in Hilbert spaces and prove spectral enclosures diagonally dominant J -self-adjoint operator matrices. These are used the proof of central result, a theorem -non-negative operators. The applied to singular indefinite Sturm-Liouville with $$L^p$$ ...

Let AN be the symmetric operator given by the restriction of A toN , where A is a self-adjoint operator on the Hilbert space H and N is a linear dense set which is closed with respect to the graph norm on D(A), the operator domain of A. We show that any self-adjoint extension AΘ of AN such that D(AΘ)∩D(A) = N can be additively decomposed by the sum AΘ = Ā + TΘ, where both the operators Ā and TΘ...