Given a self-adjoint operator A: D (A)⊆ H→ H and a continuous linear operator τ: D (A)→ X
with Range τ′∩ H′={0}, X a Banach space, we explicitly construct a family AτΘ of self …

The transformations of all the Schrödinger operators with point interactions in dimension one
under space reflection P, time reversal T and (Weyl) scaling W λ are presented. In particular …

We study a model where one target variable Y is correlated with a vector X:=(X 1,…, X d) of
predictor variables being potential causes of Y. We describe a method that infers to what …

Point interactions for the $ n $-th derivative operator in one dimension are investigated.
Every such perturbed operator coincides with a selfadjoint extension of the $ n $-th …

This monograph presents the newly developed method of rigged Hilbert spaces as a
modern approach in singular perturbation theory. A key notion of this approach is the Lax …

Abstract Non-Hermitian Hamiltonians appearing as operator realizations of-symmetric (-
symmetric in physical literature) zero-range singular perturbations of one-dimensional …

In this paper self-adjoint realizations in Hilbert and Pontryagin spaces of the formal
expression L_ α= L+ α ⟨ ⋅, φ ⟩ φ are discussed and compared. Here L is a positive self …

Gesztesy and Simon recently have proven the existence of the strong resolvent limit A∞, ω
for A α, ω= A+ α (· ω) ω, α→∞ where A is a self-adjoint positive operator, ω∈ H _-1 (H _s,\; s …

Supersingular mathcalH-n rank one perturbations of an arbitrary positive self-adjoint
operator A acting in the Hilbert space mathcalH are investigated. The operator …

Rank one perturbations of selfadjoint operators which are not necessarily semibounded are
studied in the present paper. It is proven that such perturbations are uniquely defined, if they …