Related papers: Spectral asymptotics for nonsmooth singular Green …

Let $A$ be a self-adjoint operator on a Hilbert space $\fH$. Assume that the spectrum of $A$ consists of two disjoint components $\sigma_0$ and $\sigma_1$. Let $V$ be a bounded operator on $\fH$, off-diagonal and $J$-self-adjoint with…

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…

In this paper second order elliptic boundary value problems on bounded domains $\Omega\subset\dR^n$ with boundary conditions on $\partial\Omega$ depending nonlinearly on the spectral parameter are investigated in an operator theoretic…

In a series of papers, we will develop systematically the basic spectral theory of (self-adjoint) boundary value problems for operators of Dirac type. We begin in this paper with the characterization of (self-adjoint) boundary conditions…

We introduce a calculus for parameter-dependent singular Green operators on the half-space $\mathbb{R}^n_+$ that combines both elements of Grubb's calculus for boundary value problems of finite regularity and techniques of Schulze's…

For bounded domains $\Omega$ with Lipschitz boundary $\Gamma$, we investigate boundary value problems for elliptic operators with variable coefficients of fourth order subject to Wentzell (or dynamic) boundary conditions. Using form…

Self-adjoint Schr\"odinger operators with $\delta$ and $\delta'$-potentials supported on a smooth compact hypersurface are defined explicitly via boundary conditions. The spectral properties of these operators are investigated, regularity…

Asymptotic formulae for Green's kernels $G_\epsilon({\bf x}, {\bf y})$ of various boundary value problems for the Laplace operator are obtained in regularly perturbed domains and certain domains with small singular perturbations of the…

In this paper we will study the set of parameters in which certain partial derivatives of the Green's function, related to a $n$-order linear operator $T_{n}[M]$, depending on a real parameter $M$, coupled to different two-point boundary…

In [arXiv:0801.0172] we examined a family of periodic Sturm-Liouville problems with boundary and interior singularities which are highly non-self-adjoint but have only real eigenvalues. We now establish Schatten class properties of the…

We investigate quantitative properties of nonnegative solutions $u(x)\ge 0$ to the semilinear diffusion equation $\mathcal{L} u= f(u)$, posed in a bounded domain $\Omega\subset {\mathbb R}^N$ with appropriate homogeneous Dirichlet or outer…

We consider a nonlocal differential--difference Schr\"odinger operator on a segment with the Neumann conditions and two translations in the free term. The values of the translations are denoted by $\alpha$ and $\beta$ and are treated as…

We describe a new Maple package for treating boundary problems for linear ordinary differential equations, allowing two-/multipoint as well as Stieltjes boundary conditions. For expressing differential operators, boundary conditions, and…

For a second order formally symmetric elliptic differential expression we show that the knowledge of the Dirichlet-to-Neumann map or Robin-to-Dirichlet map for suitably many energies on an arbitrarily small open subset of the boundary…

In three-dimensional case, we consider two classical operators: Schrodinger operator and an operator in the divergence form. For slowly-decaying oscillating potentials, we establish spatial asymptotics of the Green's function. The main term…

Non-self-adjoint Schrodinger operators A which correspond to non-symmetric zero-range potentials are investigated. For a given A, the description of non-real eigenvalues, spectral singularities and exceptional points are obtained; the…

Ordinary and partial differential operators with an indefinite weight function can be viewed as bounded perturbations of non-negative operators in Krein spaces. Under the assumption that 0 and $\infty$ are not singular critical points of…

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…

We show that the boundary behaviour of solutions to nonlocal fractional equations posed in bounded domains strongly differs from the one of solutions to elliptic problems modelled upon the Laplace-Poisson equation with zero boundary data.…

Let $G\subset \O(n)$ be a compact group of isometries acting on $n$-dimensional Euclidean space $\R^n$, and ${\bf{X}}$ a bounded domain in $\R^n$ which is transformed into itself under the action of $G$. Consider a symmetric, classical…