The Discreteness of the Spectrum of Self-Adjoint, Even Order, One-Term, Differential Operators

CRITICALITY OF ONE TERM 2n-ORDER SELF-ADJOINT DIFFERENTIAL EQUATIONS

where r(x) > 0, x ∈ R, and r ∈ Lloc(R). Eq. (1.1) appears as a base for perturbations in the oscillation theory, i.e., the studied equations are regarded as perturbations of Eq. (1.1). It is shown that certain properties of Eq. (1.1) are preserved or lost by perturbations. Therefore, it is useful to know as much as possible about Eq. (1.1) (to analyse its properties), see, e.g., [1, 3, 4, 5, 6,...

Non-self-adjoint Differential Operators

We describe methods which have been used to analyze the spectrum of non-self-adjoint differential operators, emphasizing the differences from the self-adjoint theory. We find that even in cases in which the eigenfunctions can be determined explicitly, they often do not form a basis; this is closely related to a high degree of instability of the eigenvalues under small perturbations of the opera...

Rank one perturbations of self-adjoint operators

the relationship between academic self-concept and academic achievement in english and general subjects of the students of high school

according to research, academic self-concept and academic achievement are mutually interdependent. in the present study, the aim was to determine the relationship between the academic self-concept and the academic achievement of students in english as a foreign language and general subjects. the participants were 320 students studying in 4th grade of high school in three cities of noor, nowshah...

Computability of the Spectrum of Self-Adjoint Operators

Self-adjoint operators and their spectra play a crucial rôle in analysis and physics. For instance, in quantum physics self-adjoint operators are used to describe measurements and the spectrum represents the set of possible measurement results. Therefore, it is a natural question whether the spectrum of a self-adjoint operator can be computed from a description of the operator. We prove that gi...