Related papers: Relaxed commutant lifting: an equivalent version a…
Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Schr\"odinger equation are considered. Due to the fact that…
We introduce and study renewal processes defined by means of extensions of the standard relaxation equation through ``stretched" non-local operators (of order $\alpha$ and with parameter $\gamma$). In a first case we obtain a generalization…
Given a Hilbert space and a finite family of operators defined on the space, the common fixed point problem (CFPP) is to find a point in the intersection of the fixed point sets of these operators. Instances of the problem have numerous…
We use a model operator approach and the spectral theorem for self-adjoint operators in a Hilbert space to derive the basic results of abstract left-definite theory in a straightforward manner. The theory is amply illustrated with a variety…
In this paper, we improve the famous Reid Inequality related to linear operators. Some monotony results for positive operators are also established with a different approach from what is known in the existing literature. Lastly, Reid and…
The aim of this article is to present two different primal-dual methods for solving structured monotone inclusions involving parallel sums of compositions of maximally monotone operators with linear bounded operators. By employing some…
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…
Recently, within the framework of the Composite Operator Method, it has been proposed a three-pole solution for the two-dimensional Hubbard model [Eur. Phys. J. B 87, 45 (2014)], which is still considered one of the best candidate model to…
Different finite difference replacements for the derivative are analyzed in the context of the Heisenberg commutation relation. The type of the finite difference operator is shown to be tied to whether one can naturally consider $P$ and $X$…
Variational regularization and the quasisolutions method are justified for unbounded closed, possibly nonlinear, operators. The argument is quite simple and yields general results.
A considerable amount of literature in the theory of inequality is devoted to the study of Jensen's and Young's inequality. This article presents a number of new inequalities involving the log-convex functions and the geometrically convex…
We consider a rather general version of ladder operator $Z$ used by some authors in few recent papers, $[H_0,Z]=\lambda Z$ for some $\lambda\in\mathbb{R}$, $H_0=H_0^\dagger$, and we show that several interesting results can be deduced from…
We show that a recent interpolative new proof of the Bohnenblust--Hille inequality, when suitably handled, recovers its best known constants. This seems to be unexpectedly surprising since the known interpolative approaches only provide…
This is the second of a series of papers surveying some small part of the remarkable work of our friend and colleague Nigel Kalton. We have written it as part of a tribute to his memory. It does not contain new results. One of the many…
In this paper, we study the operator equation $AB=\lambda BA$ for a bounded operator $A,B$ on a complex Hilbert space. We focus on algebraic relations between different operators that include normal, $M$-hyponormal, quasi $*$-paranormal and…
We consider simultaneously two different reductions of a Zakharov-Shabat's spectral problem in pole gauge. Using the concept of gauge equivalence, we construct expansions over the eigenfunctions of the recursion operators related to the…
We give a systematic treatment to the concept of hypoellipticity, putting it into an abstract form which allows us to deal with several different notions within the same framework. We then investigate when a notion of hypoellipticity…
In this paper we derive approximate quasi-interpolants when the values of a function $u$ and of some of its derivatives are prescribed at the points of a uniform grid. As a byproduct of these formulas we obtain very simple approximants…
The paper introduces a new elliptic operator called the two-radical Laplace operator, which has a positive eigenvalue equal to the positive square root of the eigenvalue of the Laplace operator. The author provide several theorems that…
We propose an approach to lifted approximate inference for first-order probabilistic models, such as Markov logic networks. It is based on performing exact lifted inference in a simplified first-order model, which is found by relaxing…