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We identify conditions giving large natural classes of partial differential operators for which it is possible to construct a complete set of Laplace invariants. In order to do that we investigate general properties of differential…
In an abstract Hilbert space setting, we discuss many linear phenomena of mathematical physics. The functional analytic framework presented is used to address continuous dependence of the solution operators $\mathcal{S}(\mathcal{M})$ of…
In this article we introduce powerful tools and techniques from invariant theory to free analysis. This enables us to study free maps with involution. These maps are free noncommutative analogs of real analytic functions of several…
We prove that the multiple summing norm of multilinear operators defined on some $n$-dimensional real or complex vector spaces with the $p$-norm may be written as an integral with respect to stables measures. As an application we show…
We state and prove a simple Theorem that allows one to generate invariant quantities in Metric-Affine Geometry, under a given transformation of the affine connection. We start by a general functional of the metric and the connection and…
We study geometric properties of varieties associated with invariant subspaces of nilpotent operators. There are reductive algebraic groups acting on these varieties. We give dimensions of orbits of these actions. Moreover, a combinatorial…
We describe all linear operators which maps $n-1$-dimensional simplex of idempotent measures to itself. Such operators divided to two classes: the first class contains all $n\times n$-matrices with non-negative entries which has at least…
We prove that canonical Dirac expression with linear potential generates operators on axis and half axis, for which we can find the eigenvalues and eigenfunctions in explicit form. We construct the perturbations of these operators with in…
We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
We systematically introduce the idea of applying differential operator method to find a particular solution of an ordinary nonhomogeneous linear differential equation with constant coefficients when the nonhomogeneous term is a polynomial…
We consider some multivariate rational functions which have (or are conjectured to have) only positive coefficients in their series expansion. We consider an operator that preserves positivity of series coefficients, and apply the inverse…
We consider the notion of the matrix (tensor) distribution of a measurable function of several variables. On the one hand, it is an invariant of this function with respect to a certain group of transformations of variables; on the other…
We study the notion of recurrence and some of its variations for linear operators acting on Banach spaces. We characterize recurrence for several classes of linear operators such as weighted shifts, composition operators and multiplication…
In this paper we explore solvability of steady-state variational inequalities with multivalued operators. Moreover, we are studying the connections between the class of radially semi-continuous operators with semi-bounded variation and…
By means of a fixed point method we discuss the deformation of operator means and multivariate means of positive definite matrices/operators. It is shown that the deformation of an operator mean becomes again an operator mean. The means…
For arbitrary linear time-invariant systems, the existence of a strong functional observer is investigated. Such observer determines, from the available measurement on the plant, an estimate of a function of the state and the input. This…
We prove the existence of the invariant subspaces of some operators in a real Banach space. For example, linear isometries have invariant subspaces
A general expression for a relative invariant of a linear ordinary differential equations is given in terms of the fundamental semi-invariant and an absolute invariant. This result is used to established a number of properties of relative…
We consider an enlarged dimension reduction space in functional inverse regression. Our operator and functional analysis based approach facilitates a compact and rigorous formulation of the functional inverse regression problem. It also…