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We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic…
Multitildes are regular operators that were introduced by Caron et al. in order to increase the number of Glushkov automata. In this paper, we study the family of the multitilde operators from an algebraic point of view using the notion of…
We define an additive version of the Bloch group of a field, together with an additive dilogarithm and an Artin-Schreier realization.
In this paper the authors show how to use Riemann-Hilbert techniques to prove various results, some old, some new, in the theory of Toeplitz operators and orthogonal polynomials on the unit circle (OPUC's). There are four main results: the…
We formulate a new class of fractional difference and sum operators, study their fundamental properties, and find their discrete Laplace transforms. The method depends on iterating the fractional sum operators corresponding to fractional…
Representations of polynomial covariance type commutation relations are constructed on Banach spaces $L_p$ and $C[\alpha, \beta],\ \alpha,\beta\in \mathbb{R}$. Representations involve operators with piecewise functions, multiplication…
The author has introduced in a recent paper a new class of operators, called co-Toeplitz operators, with symbols in a co-algebra. This is the categorical dual to Toeplitz operators which have symbols in an algebra. The mapping from a symbol…
In this paper we explore a new method of analysis of associative algebras.
Poly-infix operators and operator families are introduced as an alternative for working modulo associativity and the corresponding bracket deletion convention. Poly-infix operators represent the basic intuition of repetitively connecting an…
Exponential operator decompositions are an important tool in many fields of physics, for example, in quantum control, quantum computation, or condensed matter physics. In this work, we present a method for obtaining such decompositions,…
In this work, we propose and analyse two splitting algorithms for finding a zero of the sum of three monotone operators, one of which is assumed to be Lipschitz continuous. Each iteration of these algorithms require one forward evaluation…
In this paper we introduce an abstract approach to the notion of absolutely summing multilinear operators. We show that several previous results on different contexts (absolutely summing, almost summing, Cohen summing) are particular cases…
We study the generalization of shifted Jack polynomials to arbitrary multiplicity free spaces. In a previous paper (math.RT/0006004) we showed that these polynomials are eigenfunctions for commuting difference operators. Our central result…
This paper proposes an accelerated proximal point method for maximally monotone operators. The proof is computer-assisted via the performance estimation problem approach. The proximal point method includes various well-known convex…
A polynomial transform is the multiplication of an input vector $x\in\C^n$ by a matrix $\PT_{b,\alpha}\in\C^{n\times n},$ whose $(k,\ell)$-th element is defined as $p_\ell(\alpha_k)$ for polynomials $p_\ell(x)\in\C[x]$ from a list…
We use an interpolative technique from \cite{abps} to introduce the notion of multiple $N$-separately summing operators. Our approach extends and unifies some recent results; for instance we recover the best known estimates of the…
In this paper, we propose an algorithm combining the forward-backward splitting method and the alternative projection method for solving the system of splitting inclusion problem. We want to find a point in the interception of a finite…
We give some new characterizations of strictly Lipschitz p-summing operators. These operators have been introduced in order to improve the Lipschitz p-summing operators. Therefore, we adapt this definition for constructing other classes of…
Many mathematicians have been studying various degenerate versions of special polynomials and numbers in some arithmetic and combinatorial aspects. Our main focus here is a new type of degenerate poly-Euler polynomials and numbers. This…
In this note we augment the poly-Bernoulli family with two new combinatorial objects. We derive formulas for the relatives of the poly-Bernoulli numbers using the appropriate variations of combinatorial interpretations. Our goal is to show…