Related papers: Second-Order Differential Operators in the Limit C…

Matrix quasi exactly solvable operators are considered and new conditions are determined to test whether a matrix differential operator possesses one or several finite dimensional invariant vector spaces. New examples of $2\times 2$-matrix…

For relatively form-compact perturbations of non-negative selfadjoint operators, we obtain an upper bound on the number of discrete eigenvalues in half-planes separated from the positive real axis. The bound is given in terms of a partial…

Using an abstract notion of semiclassical quantization for self-adjoint operators, we prove that the joint spectrum of a collection of commuting semiclassical self-adjoint operators converges to the classical spectrum given by the joint…

In this paper we prove that a class of non self-adjoint second order differential operators acting in cylinders $\Omega\times\mathbb R\subseteq\mathbb R^{d+1}$ have only real discrete spectrum located to the right of the right most point of…

Closed operators in Hilbert space defined by a non-self-adjoint resolution of the identity $\{X(\lambda)\}_{\lambda\in {\mb R}}$, whose adjoints constitute also a resolution of the identity, are studied . In particular, it is shown that a…

We work with differential expressions of the form \begin{align} \tau_{2n+1} y &=(-1)^ni \{(q_{0}y^{(n+1)})^{(n)}+(q_{0}y^{(n)})^{(n+1)}\}+ \sum\limits_{k=0}^{n}(-1)^{n+k}(p^{(k)}_ky^{(n-k)})^{(n-k)} \\…

In this paper we deal with a second order multidimensional fractional differential operator. We consider a case where the leading term represented by the uniformly elliptic operator and the final term is the Kipriyanov operator of…

Supersymmetry transformations of first and second order are used to generate Hamiltonians with known spectra departing from the harmonic oscillator with an infinite potential barrier. It is studied also the way in which the eigenfunctions…

Inverse spectral problem for a self-adjoint differential operator, which is the sum of the operator of the third derivative on a finite interval and of the operator of multiplication by a real function (potential), is solved. Closed system…

The paper deals with singular Sturm-Liouville expressions with matrix-valued distributional coefficients. Due to a suitable regularization, the corresponding operators are correctly defined as quasi-differentials. Their resolvent…

The purpose of this note is to show how some results from the theory of partial differential equations apply to the study of pseudo-spectra of non-self-adjoint operators, which is a topic of current interest in applied mathematics.

We study general (not necessarily Hamiltonian) first-order symmetric systems $J y'(t)-B(t)y(t)=\D(t) f(t)$ on an interval $[a,b> $ with the regular endpoint $a$. The deficiency indices $n_\pm$ of the corresponding minimal relation $\Tmi$…

We investigate the self-adjointness of the two-dimensional Dirac operator $D$, with quantum-dot and Lorentz-scalar $\delta$-shell boundary conditions, on piecewise $C^2$ domains with finitely many corners. For both models, we prove the…

One discusses a problem of asymptotical behavior for some operators in a general theory of pseudo differential equations on manifolds with borders. Using the distribution theory one obtains certain explicit representations for these…

For a class of non-selfadjoint $h$--pseudodifferential operators with double characteristics, we give a precise description of the spectrum and establish accurate semiclassical resolvent estimates in a neighborhood of the origin.…

In this paper we consider the order-like relation for self-adjoint operators on some Hilbert space. This relation is defined by using Jensen inequality. We will show that under some assumptions this relation is antisymmetric.

We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…

We consider self-adjoint realizations of a second-order elliptic differential expression on ${\mathbb R}^n$ with singular interactions of $\delta$ and $\delta^\prime$-type supported on a compact closed smooth hypersurface in ${\mathbb…

In this study, linear second-order conformable differential equations using a proportional derivative are shown to be formally self-adjoint equations with respect to a certain inner product and the associated self-adjoint boundary…

We study self-adjoint extensions of operators which are the product of the multiplication operator by an analytic function and the analytic continuation in a strip. We compute the deficiency indices of the product operator for a wide class…