Related papers: On Generalized Powers of Operators
A quasi-product on the normed space is defined. In addition, the notions of the eigenvectors of a linear operator can be extended for the nonlinear operator. Based on the quasi-product and the generalized eigenvectors, the spectral theorems…
An important instance of Rota-Baxter algebras from their quantum field theory application is the ring of Laurent series with a suitable projection. We view the ring of Laurent series as a special case of generalized power series rings with…
Generalized spectra of differential operators can be related to spectra of preconditioned discretized operators. Obtaining (estimates of) the eigenvalues of the preconditioned discretized operators may lead to better estimating of the…
In the last decades many authors have become interested in the study of multilinear and polynomial generalizations of families of operator ideals (such as, for instance, the ideal of absolutely summing operators). However, these…
Generalized numberings are an extension of Ershov's notion of numbering, based on partial combinatory algebra (pca) instead of the natural numbers. We study various algebraic properties of generalized numberings, relating properties of the…
I consider general reflection coefficients for arbitrary one-dimensional whole line differential or difference operators of order $2$. These reflection coefficients are semicontinuous functions of the operator: their absolute value can only…
The problem of equivalency for linear differential operators of the first order is discussed.
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 $I_K$…
We consider positive, integral-preserving linear operators acting on $L^1$ space, known as stochastic operators or Markov operators. We show that, on finite-dimensional spaces, any stochastic operator can be approximated by a sequence of…
Multivalued linear operators, also known as linear relations, are studied on a specific class of weighted, composition transforms on Fock space. Basic properties of this class of linear relations, such as closed graph, boundedness, complex…
This is a survey on discrete linear operators which, besides approximating in Jackson or near-best order, possess some interpolatory property at some nodes. Such operators can be useful in numerical analysis.
Means are used in several applications from electronic engeneering to information theory, however there is no general theorem on how to extend a given M(x, y) mean function to multiple variable forms. In this article we would like to…
The new notion of operator/matrix $k$-tone functions is introduced, which is a higher order extension of operator/matrix monotone and convex functions. Differential properties of matrix $k$-tone functions are shown. Characterizations,…
In this note we introduce generalised pairs from the perspective of the evolution of the notion of space in birational algebraic geometry. We describe some applications of generalised pairs in recent years and then mention a few open…
A general deformation of the Heisenberg algebra is introduced with two deformed operators instead of just one. This is generalised to many variables, and permits the simultaneous existence of coherent states, and the transposition of…
A new understanding of the notion of regularizer is proposed. It is argued that this new notion is more realistic than the old one and better fits the practical computational needs. An example of the regularizer in the new sense is given. A…
We show that the compositions of positive integers may be interpreted in terms of powers of some power series, over arbitrary commutative ring. As consequences, several closed formulas for the compositions as well as for the generalized…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
The main aim of this paper is to generalize the classical concept of positive operator, and to develop a general extension theory, which overcomes not only the lack of a Hilbert space structure, but also the lack of a normable topology. The…
We complete the construction of raising and lowering operators, given in a previous work, for the orthogonal polynomials of hypergeometric type on non-homogeneous lattice, and extend these operators to the generalized orthogonal…