Recent work has demonstrated that Clark’s theory of unitary perturbations of the backward shift restricted to a deBranges-Rovnyak subspace of Hardy space on the disk has a natural extension to the several variable setting. In the several variable case, the appropriate generalization of the Schur class of contractive analytic functions is the closed unit ball of the Drury-Arveson multiplier alge...

It is well-known that if T is a Dm–Dn bimodule map on the m×n complex matrices, then T is a Schur multiplier and ‖T‖cb = ‖T‖. If n = 2 and T is merely assumed to be a right D2-module map, then we show that ‖T‖cb = ‖T‖. However, this property fails if m ≥ 2 and n ≥ 3. For m ≥ 2 and n = 3, 4 or n ≥ m2 we give examples of maps T attaining the supremum C(m,n) = sup{‖T‖cb : T a right Dn-module map o...

Let G be a finite p-group of order pn with |G′| = pk, and let M(G) denote its Schur multiplier. A classical result of Green states that |M(G)| ≤ p 1 2 n(n−1) . In 2009, Niroomand, improving Green’s and other bounds on |M(G)| for a non-abelian p-group G, proved that |M(G)| ≤ p 2 (n−k−1)(n+k−2)+1. In this paper, we prove that a bound, obtained earlier by Ellis and Wiegold, is stronger than that o...

0 −→ c −→ g1 φ1 −→g −→ 0 such that c ⊆ Z(g1), the center of g̃. A morphism of central extensions is a Lie algebra homomorphism ψ : g1 → g2 such that φ2ψ = φ1. A universal central extension is a central extension g̃ such that there is a unique morphism from g̃ to every other central extension of g. The Schur multiplier is the kernel of the universal central extension of g. It classifies the project...

A multivariate polynomial is stable if it is nonvanishing whenever all variables have positive imaginary parts. We classify all linear partial differential operators in the Weyl algebra An that preserve stability. An important tool that we develop in the process is the higher dimensional generalization of Pólya-Schur’s notion of multiplier sequence. We characterize all multivariate multiplier s...

A finite group G is said to be efficient if G has a presentation 〈 X | R 〉 where |R| = |X|+rank(M(G)) where M(G) is the Schur multiplier of G; see for example [14]. The efficiency of direct powers, G, of a finite group G has been studied over a number of years, see for example [5], [8] and [14]. In [6] the problem of proving that G is efficient for all n ∈ N, in the case of an imperfect group, ...

The paper is devoted to designing an interface preconditioner for the mortar element method. After brief overview of the problem in Introduction, we discuss the mortar element method with different types of the Lagrange multiplier spaces. Next, we consider the domain decomposition technique for the solution of mortar element systems and outline the general framework of the solution of saddle-po...

In this paper we present a comparison of the service disciplines in real-time queueing systems (the customers have a deadline before which they should enter the service booth). We state that the more a service discipline gives priority to customers having an early deadline, the least the average stationary lateness is. We show this result by comparing adequate random vectors with the Schur-Conv...

In this paper, using a relation between Schur multipliers of pairs and triples of groups, the fundamental group and homology groups of a homotopy pushout of Eilenberg-MacLane spaces, we present among other things some behaviors of Schur multipliers of pairs and triples with respect to free, amalgamated free, and direct products and also direct limits of groups with topological approach.