Second-Order Differential Operators in the Limit Circle Case

We consider symmetric second-order differential operators with real coefficients such that the corresponding differential equation is in the limit circle case at infinity. Our goal is to construct the theory of self-adjoint realizations of such operators by an analogy with the case of Jacobi operators. We introduce a new object, the quasiresolvent of the maximal operator, and use it to obtain a very explicit formula for the resolvents of all self-adjoint realizations. In particular, this yields a simple representation for the Cauchy-Stieltjes transforms of the spectral measures playing the role of the classical Nevanlinna formula in the theory of Jacobi operators.

Completeness Theorem for Eigenparameter Dependent Dissipative Dirac Operator with General Transfer Conditions

This paper deals with a singular (Weyl’s limit circle case) non-self-adjoint (dissipative) Dirac operator with eigenparameter dependent boundary condition and finite general transfer conditions. Using the equivalence between Lax-Phillips scattering matrix and Sz.-Nagy-Foiaş characteristic function, the completeness of the eigenfunctions and associated functions of this dissipative operator is discussed.

NONLINEAR SINGULAR STURM-LIOUVILLE PROBLEMS WITH IMPULSIVE CONDITIONS

In this paper, we consider a non-linear impulsive Sturm-Liouville problem on semiinfinite intervals in which the limit-circle case holds at infinity for THE Sturm-Liouville expression. We prove the existence and uniqueness theorems for this problem.

Titchmarsh–Weyl theory for q-Dirac systems

In this work, we establish Titchmarsh–Weyl theory for singular [Formula: see text]-Dirac systems. Thus, we extend classical Titchmarsh–Weyl theory for Dirac systems to [Formula: see text]-analogue of this system. We show that it does not occur for the limit-circle case for the [Formula: see text]-Dirac system.

“Walk the line”: An ethnographic study of the ritual of crossing the Arctic Circle—Case Rovaniemi

The Arctic Circle is the most commonly used border to delimit the Arctic region, and has been used in this way to such an extent that across the circumpolar North, municipalities and local communities have built various types of signs, shops and tourist centers for its celebration. This is especially the case in Rovaniemi, Finland, with the creation of the Santa Claus Village, “right” on the Arctic Circle, leading to several thousands of tourists crossing the magical line every year. This article focuses on tourists’ practices around Arctic Circle landmarks in Rovaniemi. This study acknowledges the hegemony of the selfie era that is indubitably linked to what is referred to in this article as “border-crossing postures”, pertaining to the ritual of performing specific practices, actions and postures that suggest the crossing of a borderline. However, it is argued that in the case of the Arctic Circle in Rovaniemi, these specific postures come from the physical aspect of the landmarks, rather than the tourists recognizing the Arctic Circle as a border.

Livšic’s theorem for q-Sturm—Liouville operators

In this paper, we study dissipative q-Sturm—Liouville operators in Weyl’s limit circle case. We describe all maximal dissipative, maximal accretive, self adjoint extensions of q-Sturm—Liouville operators. Using Livšic’s theorems, we prove a theorem on completeness of the system of eigenvectors and associated vectors of the dissipative q-Sturm—Liouville operators.

Spectral problems of nonself-adjoint singular discrete Sturm-Liouville operators

In this study we construct a space of boundary values of the minimal symmetric discrete Sturm-Liouville (or second-order difference) operators with defect index (1, 1) (in limit-circle case at ±∞ and limit-point case at ∓∞), acting in the Hilbert space