Related papers: On a group-theoretical approach to the curl operat…

There has been proposed a new method of the constructing of the basic functions for spaces of tensor representations of the Lie groups with the help of the generalized Casimir operator. In the definition of the operator there were used the…

In this short note we show that representation and character varieties of discrete groups can be viewed as tensor products of suitable functors over the PROP of cocommutative Hopf algebras. Such view point has several interesting…

A theorem that is of aid in computing the domain of the adjoint operator is provided. It may serve e.g. as a criterion for selfadjointness of a symmetric operator, for normality of a formally normal operator or for $H$--selfadjointness of…

The current paper presents a new approach to multilinear dynamical systems analysis and control. The approach is based upon recent developments in tensor decompositions and a newly defined algebra of circulants. In particular, it is shown…

The definitions and some properties (e.g. the Wigner-Eckart theorem, the fusion procedure) of covariant and contravariant q-tensor operators for quasitriangular quantum Lie algebras are formulated in the R-matrix language. The case of…

This paper investigates the eigenvalue problem of integral operators whose kernels can be expressed as a finite sum of pairwise products of single-variable functions, making them separable. By consdiering the matrix form of the separable…

This is a survey article on Mercer's Theorem in its most general form and its relations with the theory of reproducing kernel Hilbert spaces and the spectral theory of compact operators. We provide a modern introduction to the basics of the…

To be able to solve operator equations numerically a discretization of those operators is necessary. In the Galerkin approach bases are used to achieve discretized versions of operators. In a more general set-up, frames can be used to…

Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…

Given a self-adjoint operator $T$ on a separable infinite-dimensional Hilbert space we study the problem of characterizing the set $\mathcal D(T)$ of all possible diagonals of $T$. For compact operators $T$, we give a complete…

We extend the notion of the nerve of a category for a small class of crossed simplicial groups, explicitly describing them using generators and relations. We do this by first considering a generalised bar construction of a group before…

We extend the theory of distributional kernel operators to a framework of generalized functions, in which they are replaced by integral kernel operators. Moreover, in contrast to the distributional case, we show that these generalized…

In this paper, we study the consequences of the fundamental theorem of calculus from an algebraic point of view. For functions with singularities, this leads to a generalized notion of evaluation. We investigate properties of such…

We develop differential algebraic K-theory of regular arithmetic schemes. Our approach is based on a new construction of a functorial, spectrum level Beilinson regulator using differential forms. We construct a cycle map which represents…

The representation theory of tensor functions is a powerful mathematical tool for constitutive modeling of anisotropic materials. A major limitation of the traditional theory is that many point groups require fourth- or sixth-order…

We represent a matrix representation of the Neumann-Poincar\'e operator defined on the boundaries of a torus. A torus is a doubly connected domain in three dimensions. There is a well-known parametrization for the shape of the torus, the…

Several Krylov-type procedures are introduced that generalize matrix Krylov methods for tensor computations. They are denoted minimal Krylov recursion, maximal Krylov recursion, contracted tensor product Krylov recursion. It is proved that…

Given a set of matrices, modeled as samples of a matrix-valued function, we suggest a method to approximate the underline function using a product approximation operator. This operator extends known approximation methods by exploiting the…

In this paper we show how specific families of positive definite kernels serve as powerful tools in analyses of iteration algorithms for multiple layer feedforward Neural Network models. Our focus is on particular kernels that adapt well to…

The approximate representation of operators by finite matrices is analysed in terms of accuracy and convergence. The identity operator, for example, can be reconstructed using a basis of harmonic oscillator states leading to a narrow peak…