Perturbation of the spectrum οf an essentially selfadjoint operator

Spectrum Asymptotics of Airy’s Operator under Perturbation

We study the eigenvalue problem of perturbed Airy operator −4 + (x + V (x)) on positive real axis, with Dirichlet boundary condition. Given the asymptotic expansion of V (x) at +∞, we provide asymptotic expansion of the eigenvalues λn to certain order. Then we will provide an example to show that in general, merely from the asymptotic expansion of V (x), the asymptotic expansion of λn cannot be...

A selfadjoint variant of the time operator

We study the selfadjoint time operator recently constructed by one of the authors. We will show that this time operator must be interpreted as a “selfadjoint variant” of the time operator.

Spectral perturbation bounds for selfadjoint operators I∗

We give general spectral and eigenvalue perturbation bounds for a selfadjoint operator perturbed in the sense of the pseudo-Friedrichs extension. We also give several generalisations of the aforementioned extension. The spectral bounds for finite eigenvalues are obtained by using analyticity and monotonicity properties (rather than variational principles) and they are general enough to include ...

The Laplace operator is essentially self-adjoint

The essentially free spectrum of a variety

We partially prove a conjecture from [MeSh] which says that the spectrum of almost free, essentially free, non-free algebras in a variety is either empty or consists of the class of all successor cardinals. Introduction and notation Suppose that T is a variety in a countable vocabulary τ . This means that τ is a countable set of function symbols and T is a set of equations, i.e. sentences of th...