Related papers: S-Spectrum and the quaternionic Cayley transform o…
Yang-Baxter R operators symmetric with respect to the orthogonal and symplectic algebras are considered in an uniform way. Explicit forms for the spinorial and metaplectic R operators are obtained. L operators, obeying the RLL relation with…
An absolute continuity approach to quasinormality which relates the operator in question to the spectral measure of its modulus is developed. Algebraic characterizations of some classes of operators that emerged in this context are…
This paper outlines a covariant theory of operators defined on groups and homogeneous spaces. A systematic use of groups and their representations allows to obtain results of algebraic and analytical nature. The consideration is…
In this paper we examine the asymptotic structure of the pseudospectrum of the singular Sturm-Liouville operator $L=\partial_x(f\partial_x)+\partial_x$ subject to periodic boundary conditions on a symmetric interval, where the coefficient…
This is the first step in an attempt at a deformation theory for $G_{2}-$instantons with $1-$dimensional conic singularities. Under a set of model data, the linearization yields a self-adjoint first order elliptic operator $P$ on a certain…
We study the most general continuous transformation on the generators of bilinear master equations of a quantum oscillator. We find that transformation operators that preserve the hermiticity of density operators and conserve the…
In general case of deformed Heisenberg algebra leading to the minimal length we present a definition of the square inverse position operator. Our proposal is based on the functional analysis of the square position operator. Using this…
The quaternionic KP hierarchy is the integrable hierarchy of p.d.e obtained by replacing the complex numbers with the quaternions, mutatis mutandis, in the standard construction of the KP hierarchy equations and solutions; it is equivalent…
We consider the complex solvable non-commutative two dimensional Lie algebra $L$, $L=<y>\oplus <x>$, with Lie bracket $[x,y]=y$, as linear bounded operators acting on a complex Hilbert space $H$. Under the assumption $R(y)$ closed, we…
The description of all correct restrictions of the maximal operator are considered in a Hilbert space. A class of correct restrictions are obtained for which a similar transformation has the domain of the fixed correct restriction. The…
In this paper, we use four-dimensional quaternionic algebra to describing space-time field equations in curvature form. The transformation relations of a quaternionic variable are established with the help of basis transformations of…
We discuss some of the analytic properties of lens space indices for 4d N=2 theories of class S. The S-duality properties of these theories highly constrain the lens space indices, and imply in particular that they are naturally acted upon…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces i.e.; spaces generated by positive semidefinite sesquilinear forms. Let H be a Hilbert space and let A be a positive bounded operator on H…
We establish a spectral characterization theorem for the operators on complex Hilbert spaces of arbitrary dimensions that attain their norm on every closed subspace. The class of these operators is not closed under addition. Nevertheless,…
we start the study of Schur analysis in the quaternionic setting using the theory of slice hyperholomorphic functions. The novelty of our approach is that slice hyperholomorphic functions allows to write realizations in terms of a suitable…
Affiliated and normal operators in octonion Hilbert spaces are studied. Theorems about their properties and of related algebras are demonstrated. Spectra of unbounded normal operators are investigated.
In this article we give an approach to define continuous functional calculus for bounded quaternionic normal operators defined on a right quaternionic Hilbert space.
A spectral theory of linear operators on rigged Hilbert spaces (Gelfand triplets) is developed under the assumptions that a linear operator $T$ on a Hilbert space $\mathcal{H}$ is a perturbation of a selfadjoint operator, and the spectral…
We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…