Related papers: On Titchmarsh-Weyl functions and eigenfunction exp…

We study the isospectrality problem for a relativistic free quantum particle, described by the Dirac Hamiltonian, confined in a one-dimensional ring with a junction. We analyze all the self-adjoint extensions of the Hamiltonian in terms of…

M.Levitin and E.Shargorodsky purposed in a recent article, [math.SP/0212087], the use of the so called ``second order relative spectrum'', to find eigenvalues of self-adjoint operators in gaps of the essential spectrum. Let $M$ be a…

We establish a mutual relationship between main analytic objects for the dissipative extension theory of a symmetric operator $\dot A$ with deficiency indices $(1,1)$. In particular, we introduce the Weyl-Titchmarsh function $\cM$ of a…

The main purpose of this paper is to investigate the formal deficiency indices ${\cal N}_{\pm}(I)$ of a symmetric first order system $$ Jf'+Bf=\lambda {\cal H} f $$ on an interval $I$, where $I=\mathbb{R}$ or $I=\mathbb{R}_\pm.$ Here…

In this study, we are concerned with spectral problems of second-order vector dynamic equations with two-point boundary value conditions and mixed derivatives, where the matrix-valued coefficient of the leading term may be singular, and the…

We consider a certain class of Herglotz-Nevanlinna matrix-valued functions which can be realized as the Weyl-Titchmarsh matrix-valued function of some symmetric operator and its self-adjoint extension. New properties of Weyl -Titchmarsh…

We establish existence and uniqueness results for nonlinear elliptic Dirichlet boundary value problems on n-dimensional time scale domains. Time scales provide a unified framework that encompasses continuous, discrete, and hybrid settings.…

Let $A$ be a densely defined symmetric operator with equal deficiency indices in a Hilbert space. We introduce the notion of a Weyl function $M(z)$ of $A$ corresponding to an ordinary boundary triplet of the operator $A^*$ and then…

This paper deals with the Sturm-Liouville problem that feature distribution potential, polynomial dependence on the spectral parameter in the first boundary condition, and analytical dependence, in the second one. We study an inverse…

We provide a comparative treatment of some aspects of spectral theory for self-adjoint and non-self-adjoint (but J-self-adjoint) Dirac-type operators connected with the defocusing and focusing nonlinear Schr\"odinger equation, of relevance…

A Lax-Oleinik type explicit formula for 1D scalar balance laws has been recently obtained for the pure initial value problem by Adimurthi et al. in [1]. In this article, by introducing a suitable boundary functional, we establish a…

In this paper we solve the eigenvalue problem of stochastic Hamiltonian system with boundary conditions. Firstly, we extend the results in S. Peng \cite{peng} from time-invariant case to time-dependent case, proving the existence of a…

In the paper, we use $\mathrm{U}(2)$, the group of $2\times 2$ unitary matices, to parameterize the space of all self-adjoint boundary conditions for a fixed Sturm-Liouville equation on the interval $[0,1]$. The adjoint action of…

We study realizations generated by the original Weyl-Titchmarsh functions $m_\infty(z)$ and $m_\alpha(z)$. It is shown that the Herglotz-Nevanlinna functions $(-m_\infty(z))$ and $(1/m_\infty(z))$ can be realized as the impedance functions…

This paper is related to an inverse problem for a class of Dirac operators with discontinuous coefficient and eigenvalue parameter contained in boundary conditions. The asymptotic formula of eigenvalues of this problem is examined. The…

We consider the nonlinear boundary value problem consisting of the equation \tag{1} -u" = f(u) + h, \quad \text{a.e. on $(-1,1)$,} where $h \in L^1(-1,1)$, together with the multi-point, Dirichlet-type boundary conditions \tag{2} u(\pm 1) =…

The transmission problem is a system of two second-order elliptic equations of two unknowns equipped with the Cauchy data on the boundary. After four decades of research motivated by scattering theory, the spectral properties of this…

We study two problems. The first one is the similarity problem for the indefinite Sturm-Liouville operator \[ A=-(\sgn\, x)\frac{d}{wdx}\frac{d}{rdx} \] acting in $L^2_{w}(-b,b)$. It is assumed that $w,r\in L^1_{\loc}(-b,b)$ are even and…

In this paper we study the almost everywhere convergence of the expansions related to the self-adjoint extension of the Laplace-Beltrami operator on the unit sphere. The sufficient conditions for summability is obtained. The more general…

In this paper following the same methods in [M. Kadakal, O. Sh. Mukhtarov, Sturm-Liouville problems with discontinuities at two points, Comput. Math. Appl., 54 (2007) 1367-1379] we investigate discontinuous two-point boundary value problems…