Related papers: Polynomial inequalities for non-commuting operator…
We present a new, elementary proof of Boyd's interpolation theorem. Our approach naturally yields a noncommutative version of this result and even allows for the interpolation of certain operators on l^1-valued noncommutative symmetric…
In this paper we extend a recent Pisier's inequality for p-orthogonal sums in non-commutative Lebesgue spaces. To that purpose, we generalize the notion of p-orthogonality to the class of multi-indexed families of operators. This kind of…
We consider symmetric polynomials, p, in the noncommutative free variables (x_1, x_2, ..., x_g). We define the noncommutative complex hessian of p and we call a noncommutative symmetric polynomial noncommutative plurisubharmonic if it has a…
In this paper we present equivalence results for several types of unbounded operator functions. A generalization of the concept equivalence after extension is introduced and used to prove equivalence and linearization for classes of…
In this paper, the new weighted inequalities were derived by-distance which is similar to the given inequality for the potential operator defined in [1].
We use linear algebraic methods to obtain general results about linear operators on a space of polynomials that we apply to the operators associated with a polynomial sequence by the monomiality property. We show that all such operators are…
Variational inequalities offer a versatile and straightforward approach to analyzing a broad range of equilibrium problems in both theoretical and practical fields. In this paper, we consider a composite generally non-monotone variational…
It is shown how to compute quotients efficiently in non-commutative univariate polynomial rings. This extends earlier work where efficient generic quotients were studied with a primary focus on commutative domains. Fast algorithms are given…
We use a polynomial decomposition result by Stapledon to show that the numerator polynomial of the Ehrhart series of an open polytope is the difference of two symmetric polynomials with nonnegative integer coefficients. We obtain a related…
We prove Bloom type two-weight inequalities for commutators of multilinear singular integral operators including Calder\'on-Zygmund operators and their dyadic counterparts. Such estimates are further extended to a general higher order…
The detailed construction of the general solution of a second order non-homogenous linear operatordifference equation is presented. The wide applicability of such an equation as well as the usefulness of its resolutive formula is shown by…
In this paper, we prove some Hermite-Hadamard type inequalities for operator geometrically convex functions for non-commutative operators. Keywords: Operator geometrically convex function, Hermite-Hadamard inequality.
We study non-symmetric Jacobi polynomials of type $BC_{1}$ by means of vector-valued and matrix-valued orthogonal polynomials. The interpretation as matrix-valued orthogonal polynomials yields a new expression of the non-symmetric Jacobi…
In this paper we introduce and investigate a one-parameter family of polynomials. They are semisymmetric, i.e. symmetric in the variables with odd and even index separately. In fact, the family forms a basis of the space of semisymmetric…
With techniques borrowed from quantum information theory, we develop a method to systematically obtain operator inequalities and identities in several matrix variables. These take the form of trace polynomials: polynomial-like expressions…
The elements of the class of non-homogeneous differential operators which are based on the same vector field, when viewed as acting on appropriate Hilbert spaces, are shown to be isomorphic to each other. It shown that the replacement of a…
In this paper we explore solvability of steady-state variational inequalities with multivalued operators. Moreover, we are studying the connections between the class of radially semi-continuous operators with semi-bounded variation and…
We study the polynomial approximation of symmetric multivariate functions and of multi-set functions. Specifically, we consider $f(x_1, \dots, x_N)$, where $x_i \in \mathbb{R}^d$, and $f$ is invariant under permutations of its $N$…
Nonsymmetric Askey-Wilson polynomials are usually written as Laurent polynomials. We write them equivalently as 2-vector-valued symmetric Laurent polynomials. Then the Dunkl-Cherednik operator of which they are eigenfunctions, is…
We consider space-saving versions of several important operations on univariate polynomials, namely power series inversion and division, division with remainder, multi-point evaluation, and interpolation. Now-classical results show that…