相关论文: Multi-indexed p-orthogonal sums in non-commutative…
We give two examples of algebras of differential operators associated to families of matrix valued orthogonal polynomials arising from representations of SU$(N+1)$. The first one gives a commutative algebra and the second one a…
Among all states on the algebra of non-commutative polynomials, we characterize the ones that have monic orthogonal polynomials. The characterizations involve recursion relations, Hankel-type determinants, and a representation as a joint…
In this paper we use the orthogonal system of the Jacobi polynomials as a tool to study the Riemann-Liouville fractional integral and derivative operators on a compact of the real axis.This approach has some advantages and allows us to…
In this paper we introduce a notion of duality for matrix valued orthogonal polynomials with respect to a measure supported on the nonnegative integers. We show that the dual families are closely related to certain difference operators…
We derive a family of weighted Hardy-type inequalities in the variable exponent Lebesgue space with an additional term of the form \[ \int_\Omega\ |\xi|^{p(x)} \mu_{1,\beta}(dx)\leqslant \int_\Omega |\nabla…
The aim of this article is to prove a representation theorem for orthogonally additive polynomials in the spirit of the recent theorem on representation of orthogonally additive polynomials on Banach lattices but for the setting of Riesz…
In this paper we will establish different weighted Poincar\'{e} inequalities with variable exponents on Carnot-Carath\'{e}odory spaces or Carnot groups. We will use different techniques to obtain these inequalities. For vector fields…
We consider arbitrary algebraic families of lower order deformations of nondegenerate toric exponential sums over a finite field. We construct a relative polytope with the aid of which we define a ring of coefficients consisting of p-adic…
Let $(X,d,\mu)$ denotes non-homogeneous metric measure space satisfying geometrically doubling and the upper doubling measure condition. In this paper, the boundedness in Lebesgue spaces for two kinds of commutators, which are iterated…
Pisier's inequality is central in the study of normed spaces and has important applications in geometry. We provide an elementary proof of this inequality, which avoids some non-constructive steps from previous proofs. Our goal is to make…
This article provides a synthesis of recent advances in the study of the PI property in various classes of noncommutative algebras of polynomial type.
Studies the cohomology of p-central, powerful, p-groups with a certain extension property. These groups are naturally associated to Lie algebras. The paper develops a machinery that calculates the first few terms of the Bockstein spectral…
We consider orthogonal polynomials with respect to a linear differential operator $$\mathcal{L}^{(M)}=\sum_{k=0}^{M}\rho_{k}(z)\frac{d^k}{dz^k}, $$ where $\{\rho_k\}_{k=0}^{M}$ are complex polynomials such that $deg[\rho_k]\leq k, 0\leq k…
We derive sharp, explicit constants in inverse trace inequalities for polynomial functions belonging to $\mathbb{P}_p(T)$ (polynomial space with total degree $p$) that are orthogonal to the lower-order subspace $\mathbb{P}_n(T)$, $n\leq p$,…
Given a collection P of k^2 commutative polynomials in 2k^2 commutative variables, the objective is to find a condensed representation of these polynomials in terms of a single non-commutative polynomial p(X,Y) in two k x k matrix variables…
We apply the geometric approach provided by $\Sigma$-operators to develop a theory of $p$-summability for multilinear operators. In this way, we introduce the notion of Lipschitz $p$-summing multilinear operators and show that it is…
In this work we found order estimates for the upper bounds of the deviations of analogue of Zigmund's sums on the classes of $(\psi;\beta)$-differentiable functions in the metrics of generalized Lebesgue spaces with variable exponent.
We study a new family of q-Meixner multiple orthogonal polynomials of the first kind. The discrete orthogonality conditions are considered over a non-uniform lattice with respect to different q-analogues of Pascal distributions. We address…
Inspired by the commutator and anticommutator algebras derived from algebras graded by groups, we introduce noncommutatively graded algebras. We generalize various classical graded results to the noncommutatively graded situation concerning…
In this paper we present some new identities of hypergeometric type for multiple harmonic sums whose indices are the sequences $(\{1\}^a,c,\{1\}^b),$ $(\{2\}^a,c,\{2\}^b)$ and prove a number of congruences for these sums modulo a prime $p.$…