Related papers: Isoperimetric inequalities for some integral opera…
We reflect real spectra of new logarithmic model PT-symmetry operators with singular and non-singular in nature. We also notice that iso-spectral nature between inverted and non-inverted logarithmic PT-symmetric potentials. Present…
Motivated by the study of spectral properties of self-adjoint operators in the integral group ring of a sofic group, we define and study integer operators. We establish a relation with classical potential theory and in particular the circle…
This is Part 1 of two papers where we develop the basic potential theory of elliptic operators on posssibly singular almost minimzers using their hyperbolic unfoldings. We can establish surprisingly robust boundary Harnack inequalities…
We turn back to some pioneering results concerning, in particular, nonlinear potential theory and non-homogeneous boundary value problems for the so called p-Laplacian operator. Unfortunately these results, obtained at the very beginning of…
We consider the problem of estimating the eigenvalues and the integral of the corresponding eigenfunctions, associated to the Newtonian potential operator, defined in a bounded domain $\Omega \subset \mathbb{R}^{d},$ where $d = 2, 3$, in…
Existence results for a class of Choquard equations with potentials are established. The potential has a limit at infinity and it is taken invariant under the action of a closed subgroup of linear isometries of $\mathbb{R}^N$. As a…
Some elementary inequalities providing upper bounds for the difference of the norm and the numerical radius of a bounded linear operator on Hilbert spaces under appropriate conditions are given.
Inverse spectral problems for Sturm-Liouville operators on a finite interval with non-separated boundary conditions are studied in the central symmetric case, when the potential is symmetric with respect to the middle of the interval. We…
The main purpose of this paper is to establish some isoperimetric type inequalities for mappings induced by the weighted Laplace differential operators. The obtained results of this paper provide improvements and extensions of the…
The primary purpose of this paper is to investigate the question of invertibility of the sum of operators. The setting is bounded and unbounded linear operators. Some interesting examples and consequences are given. As an illustrative…
A general form for ladder operators is used to construct a method to solve bound-state Schr\"odinger equations. The characteristics of supersymmetry and shape invariance of the system are the start point of the approach. To show the…
In this review paper we carry on our investigations on Schroedinger operators with inverse square potentials on the half-line. Depending on several parameters, such operators possess either a finite number of complex eigenvalues, or an…
In this paper, the new weighted inequalities were derived by-distance which is similar to the given inequality for the potential operator defined in [1].
We consider linear and obstacle problems driven by a nonlocal integral operator, for which nonlocal interactions are restricted to a ball of finite radius. These type of operators are used to model anomalous diffusion and, for a special…
We present maximality results in the setting of non necessarily bounded operators. In particular, we discuss and establish results showing when the "inclusion" between operators becomes a full equality.
We develop a systematic approach to construct novel completely solvable rational potentials. Second-order supersymmetric quantum mechanics dictates the latter to be isospectral to some well-studied quantum systems. $\cal PT$ symmetry may…
We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to…
We consider the self-adjoint Dirac operators on a finite interval with summable matrix-valued potentials and general boundary conditions. For such operators, we study the inverse problem of reconstructing the potential and the boundary…
Potential theory on the complement of a subset of the real axis attracts a lot of attention both in function theory and applied sciences. The paper discusses one aspect of the theory - the logarithmic capacity of closed subsets of the real…
In this article, we study quasi-isospectral operators as a generalization of isospectral operators. The paper contains both expository material and original results. We begin by reviewing known results on isospectral potentials on compact…