Spectral stability analysis for solitary waves is developed in the context of the Hamiltonian system of coupled nonlinear Schrödinger equations. The linear eigenvalue problem for a non-self-adjoint operator is studied with two self-adjoint matrix Schrödinger operators. Sharp bounds on the number and type of unstable eigenvalues in the spectral problem are found from the inertia law for quadrati...

Adjoint state method is a well-known method to efficiently compute the gradient of a cost or objective function for a simulation-driven optimization problem. Essentially, it computes the adjoint action of Born operator (the linearized forward map) on any given vector. This report presents a derivation of adjoint state algorithm for an acoustic system discretized by staggered grid finite differe...

We consider a singular Sturm-Liouville differential expression with an indefinite weight function and we show that the corresponding self-adjoint differential operator in a Krein space locally has the same spectral properties as a definitizable operator.

We introduce the notion of formally self-adjoint conformally covariant polydifferential operators and give some constructions families such operators. In one direction, we show that any homogeneous variational scalar Riemannian invariant (CVI) induces these another use ambient metric to alternative certain produced this way, which is a self-adjoint, fourth-order, tridifferential operator should...

The article is devoted to building various dilatations of linear operators. explicit construction a unitary dilation compression operator considered. Then the J-unitary dilatation bounded constructed by means knot concept operator. Using Pavlov method, we construct self-adjoint dissipative We consider spectral and translational representations densely defined with nonempty set regular points. a...

We discuss the division method for subspectra which appears to be one of the key approaches in the study of spectral properties of self-adjoint differential vector-operators, that is operators generated as a direct sum of self-adjoint extensions on an Everitt-Markus-Zettl multi-interval system. In the current work we show how the division method may be applied to obtain the ordered spectral rep...

For a class of singular potentials, including the Coulomb potential and V (x) = g/x with the coefficient g in a certain range, the corresponding Schrödinger operator is not automatically self-adjoint on its natural domain. Such operators admit more than one self-adjoint domain, and the spectrum and all physical consequences depend seriously on the selfadjoint version chosen. The talk discusses ...

Let M be a complete Riemannian manifold and D : C∞ 0 (E) → C∞ 0 (F ) a first order differential operator acting between sections of the hermitian vector bundles E, F . Moreover, let V : C∞(E) → L∞ loc (E) be a self–adjoint zero order differential operator. We give a sufficient condition for the Schrödinger operator H = DD + V to be essentially self–adjoint. This generalizes recent work of I. Ol...

Given two self-adjoint, positive, compact operators A,B on a separable Hilbert space, we show that there exists a self-adjoint, positive, compact operator C commuting with B such that limt→∞ ||(e Bt 2 ee Bt 2 ) 1 t − e || = 0. 1

Pauli’s well known theorem (W. Pauli, Hanbuch der Physik vol. 5/1, ed. S. Flugge, (1926) p.60) asserts that the existence of a self-adjoint time operator canonically conjugate to a given Hamiltonian implies that the time operator and the Hamiltonian posses completely continuous spectra spanning the entire real line. Thus the conclusion that there exists no self-adjoint time operator conjugate t...