Related papers: Free cumulants, Schr\"oder trees, and operads
In this paper we investigate the properties of the free Sheffer systems, which are certain families of martingale polynomials with respect to the free Levy processes. First, we classify such families that consist of orthogonal polynomials;…
In this paper we use the viewpoint of the formal calculus underlying vertex operator algebra theory to study certain aspects of the classical umbral calculus and we introduce and study certain operators generalizing the classical umbral…
By representing elements in free fields (over a commutative field and a finite alphabet) using Cohn and Reutenauer's linear representations, we provide an algorithmic construction for the (partial) non-commutative (or Hausdorff-) derivative…
In this paper, the Composition-Diamond lemma for commutative algebras with multiple operators is established. As applications, the Gr\"obner-Shirshov bases and linear bases of free commutative Rota-Baxter algebra, free commutative…
In this work, we generalize previous results about the Fractionary Schr\"{o}dinger Equation within the formalism of the theory of Tempered Ultradistributions. Several examples of the use of this theory are given. In particular we evaluate…
Free variables occur frequently in mathematics and computer science with ad hoc and altering semantics. We present the most recent version of our free-variable framework for two-valued logics with properly improved functionality, but only…
The theory of abstract Friedrichs operators, introduced by Ern, Guermond and Caplain (2007), proved to be a successful setting for studying positive symmetric systems of first order partial differential equations (Friedrichs, 1958),…
We give a nonrecursive, combinatorial characterization of multiplicity-free products of Grassmannian Schubert classes. This answers a question of W. Fulton and extends results of J. Stembridge.
We establish a platform to transfer $L_p$-completely bounded maps on tensor products of von Neumann algebras to $L_p$-completely bounded maps on the corresponding amalgamated free products. As a consequence, we obtain a H\"ormander-Mikhlin…
We consider algebras of rational power series over an alphabet $\Sigma$ with coefficients in a commutative semiring $K$ and characterize them as the free algebras in various classes of algebraic structures.
A class of algebras is constructed using free fermions and the invariant antisymmetric tensors associated with irreducible holonomy groups. (This version contains minor typographical corrections and some additional references. )
Any non-residually finite Baumslag-Solitar group has a non-residually finite image in the abstract commensuration of a nonabelian free group. This gives a new proof (avoiding Britton's Lemma) of the classification of residually finite…
In this paper we collect a few results about exchangeability systems in which crossing cumulants vanish, which we call noncrossing exchangeability systems. The main result is a free version of De Finetti's theorem, characterising…
Although in general there is no meaningful concept of factorization in fields, that in free associative algebras (over a commutative field) can be extended to their respective free field (universal field of fractions) on the level of…
Let $\M(A,\theta)$ be a free partially commutative monoid. We give here a necessary and sufficient condition on a subalphabet $B\subset A$ such that the right factor of a bisection $\M(A,\theta)=\M(B,\theta\_B).T$ be also partially…
This paper studies which functions computed by $\mathbb{Z}$-weighted automata can be realized by $\mathbb{N}$-weighted automata, under two extra assumptions: commutativity (the order of letters in the input does not matter) and polynomial…
We introduce a class of operators associated with the signature of a smooth path $X$ with values in a $C^{\star}$ algebra $\mathcal{A}$. These operators serve as the basis of Taylor expansions of solutions to controlled differential…
We study arbitrary order symmetry operators for the linear Schr\"odinger equations with arbitrary number of spatial variables. We deduce determining equations for coefficient functions of such operators and consider in detail some cases…
We demonstrate that the notions of bi-free independence and combinatorial-bi-free independence of two-faced families are equivalent using a diagrammatic view of bi-non-crossing partitions. These diagrams produce an operator model on a Fock…
The present paper is mainly concerned with equations involving exponentials of bounded normal operators. Conditions implying commutativity of those normal operators are given. This is carried out without the known $2\pi i$-congruence-free…