A remark on probabilistical definiteness for self-adjoint operators

Adjoint and self - adjoint differential operators on graphs ∗

A differential operator on a directed graph with weighted edges is characterized as a system of ordinary differential operators. A class of local operators is introduced to clarify which operators should be considered as defined on the graph. When the edge lengths have a positive lower bound, all local self-adjoint extensions of the minimal symmetric operator may be classified by boundary condi...

A Note on Jensen Inequality for Self-adjoint Operators

In this paper we consider the order-like relation for self-adjoint operators on some Hilbert space. This relation is defined by using Jensen inequality. We will show that under some assumptions this relation is antisymmetric.

On Families of Self Adjoint Operators

Self-adjoint operators on surfaces in Rn

Our aim in this paper is to define principal and characteristic directions at points on a smooth 2-dimensional surface in the Euclidean space R in such a way that their equations together with that of the asymptotic directions behave in the same way as the triple formed by their counterpart on smooth surfaces in the Euclidean space R. The definitions we propose are derived from a more general a...

Stability indices for constrained self-adjoint operators

A wide class of problems in the study of the spectral and orbital stability of dispersive waves in Hamiltonian systems can be reduced to understanding the so-called “energy spectrum,” that is the spectrum of the second variation of the Hamiltonian evaluated at the wave shape, which is constrained to act on a closed subspace of the underlying Hilbert space. We present a substantially simplified ...