Related papers: Generalized resolvents of symmetric and isometric …
Despite the number of relevant considerations in the literature, the algebra of generalized symmetries of the Burgers equation has not been exhaustively described. We fill this gap, presenting a basis of this algebra in an explicit form and…
We study generalized solutions of an evolutionary equation related to a densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and find…
We investigate the generalized quadratic operator defined by $$T =\left( \begin{array}{cc} a I_H & A \\ c A^* & bI_K \end{array} \right) ,$$ where $H$ and $K$ are Hilbert spaces, $A:K\to H$ is a bounded linear operator, $I_H$ and $I_K$…
Using an original method, we find the algebra of generalized symmetries of a remarkable (1+2)-dimensional ultraparabolic Fokker-Planck equation, which is also called the Kolmogorov equation and is singled out within the entire class of…
An isometric operator V in a Pontryagin space H is called standard, if its domain and the range are nondegenerate subspaces in H. A description of coresolvents for standard isometric operators is known and basic underlying concepts that…
We propose a definition of deformed symmetrizable generalized Cartan matrices with several deformation parameters, which admit a categorical interpretation by graded modules over the generalized preprojective algebras in the sense of…
We study a specific family of symmetric norms on the algebra $\mathcal B(\mathcal H)$ of operators on a separable infinite-dimensional Hilbert space. With respect to each symmetric norm in this family the identity operator fails to attain…
The Volterra-type integral operator plays an essential role in modern complex analysis and operator theory. Recently, Chalmoukis \cite{Cn} introduced a generalized integral operator, say $I_{g,a}$, defined by…
In the contest of open quantum systems, we study a class of Kraus operators whose definition relies on the defining representation of the symmetric groups. We analyze the induced orbits as well as the limit set and the degenerate cases.
We consider resolvents of operators taking the form ${\bf A}=\Gamma_1{\bf B}\Gamma_1$ where $\Gamma_1({\bf k})$ is a projection that acts locally in Fourier space and ${\bf B}({\bf x})$ is an operator that acts locally in real space. Such…
A generalization with singular weights of Moore-Penrose generalized inverses of closed range operators in Hilbert spaces is studied using the notion of compatibility of subspaces and positive operators.
We consider a generalized discriminant associated to a symmetric space which generalizes the discriminant of real symmetric matrices, and note that it can be written as a sum of squares of real polynomials. A method to estimate the minimum…
This paper is devoted to strictly hyperbolic systems and equations with non-smooth coefficients. Below a certain level of smoothness, distributional solutions may fail to exist. We construct generalised solutions in the Colombeau algebra of…
The main objects of our considerations are differential operators generated by a formally selfadjoint differential expression of an even order on the interval $[0,b> (b\leq \infty)$ with operator valued coefficients. We complement and…
The paper develops a theory of spectral boundary value problems from the perspective of general theory of linear operators in Hilbert spaces. An abstract form of spectral boundary value problem with generalized boundary conditions is…
The classical Kramer sampling theorem establishes general conditions that allow the reconstruction of functions by mean of orthogonal sampling formulae. One major task in sampling theory is to find concrete, non trivial realizations of this…
We present a generalization of Krein-\v{S}mul'jan theorem which involves several operators. Given bounded selfadjoint operators $A,B_1,\ldots,B_m$ acting on a Hilbert space $\mathcal{H}$, we provide sufficient conditions to determine…
Let V be a unitary space. Suppose G is a subgroup of the full symmetric group S_m and X is an irreducible unitary representation of G. In this paper, we introduce the generalized Cartesian symmetry class over V associated with G and X. Then…
We study symmetric and antisymmetric tensor products of Hilbert-space operators, focusing on norms and spectra for some well-known classes favored by function-theoretic operator theorists. We pose many open questions that should interest…
Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…