Related papers: The Cesaro operator
In this paper, we investigate the power of nearly purely operational techniques in the study of umbral calculus. We present a concise reconstruction of the theory based on a systematic use of linear operators, with particular attention to…
In this brief note the operatorial methods are applied to the study of the Airy function and its generalizations.
The operator nabla, introduced by Garsia and the author, plays a crucial role in many aspect of the study of diagonal harmonics. Besides giving several new formulas involving this operator, we show how one is lead to representation…
Ces\`aro $(C,\delta)$ means are studied for orthogonal expansions with respect to the weight function $\prod_{i=1}^{d}|x_i|^{2\k_i}$ on the unit sphere, and for the corresponding weight functions on the unit ball and the Jacobi weight on…
We survey the model theory of operator systems and C$^*$-algebras.
In this exposition, I discuss several developments in the theory of vertex operator algebras, and I include motivation for the definition.
The tools, ideas, and insights from linear algebra, abstract algebra, and functional analysis can be extremely useful to signal processing and system theory in various areas of engineering, science, and social science including…
We consider all genus zero and genus one correlation functions for the Virasoro vacuum descendants of a vertex operator algebra. These are described in terms of explicit generating functions that can be combinatorially expressed in terms of…
In this master thesis, I discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science.
In this paper, we study the existence of solutions of some kinds of operator equations via operator inequalities. First, we investigate characterizations of operator order $A\geqslant B >0$ and chaotic operator order log $A \geqslant$ log…
This paper explores the Invariant Subspace Problem in operator theory and functional analysis, examining its applications in various branches of mathematics and physics. The problem addresses the existence of invariant subspaces for bounded…
This paper presents some properties and applications of "transversal operators". Two transversal operators are presented: a "translation" operator T and a "dilation" operator D. Such operators are used in common analysis systems including…
We overview the development of Fra\"{i}ss\'e theory in the setting of continuous model theory, and some of the its recent applications to $\mathrm{C}^*$-algebra theory and functional analysis.
We extend the well-known Katznelson-Tzafriri theorem, originally posed for power-bounded operators, to the case of Ces\`aro bounded operators of any order $\alpha>0.$ For this purpose, we use a functional calculus between a new class of…
This survey on approximations of perturbed operator functions addresses recent advances and some of the successful methods.
There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.
This paper explores various classes of invariant subspaces of the classical Ces\`{a}ro operator $C$ on the Hardy space $H^2$. We provide a new characterization of the finite co-dimensional $C$-invariant subspaces, based on earlier work of…
In this paper the spectrum of composition operators on the space of real analytic functions is investigated. In some cases it is completely determined while in some other cases it is only estimated.
In this second of three introductory papers, we extend the notion of generalised Cesaro summation/convergence to the more natural setting of what we call remainder Cesaro summation/convergence. This greatly expands the range of problems…
This survey provides an overview of common applications, both implicit and explicit, of "tensors" and "tensor products" in the fields of data science and statistics. One goal is to reconcile seemingly distinct usages of the term "tensor" in…