We describe the classical o(3, 2) r-matrices as generating the quantum deformations of either D=3 conformal algebra with mass-like deformation parameters or D=4 AdS algebra with dimensionless deformation parameters. We describe the quantization of classical o(3, 2) r-matrices via Drinfeld twist method which locates the deformation in the coalgebra sector. Further we obtain the quantum o(3, 2) a...

We describe the classical o(3, 2) r-matrices as generating the quantum deformations of either D=3 conformal algebra with mass-like deformation parameters or D=4 AdS algebra with dimensionless deformation parameters. We describe the quantization of classical o(3, 2) r-matrices via Drinfeld twist method which locates the deformation in the coalgebra sector. Further we obtain the quantum o(3, 2) a...

The authors prove that bilinear operators given by finite sums of products of Calderón-Zygmund operators on Rn are bounded from HK̇11 q1 × HK̇ α2,p2 q2 into HK̇ q if and only if they have vanishing moments up to a certain order dictated by the target space. Here HK̇ q are homogeneous Herz-type Hardy spaces with 1/p = 1/p1 +1/p2, 0 < pi ≤ ∞, 1/q = 1/q1 +1/q2, 1 < q1, q2 < ∞, 1 ≤ q < ∞, α = α1 + α2 a...

This paper investigates both the H∞ and robust H∞ reduced order unbiased filtering problems for respectively a nominal bilinear system and a bilinear system affected by norm-bounded structured uncertainties in all the system matrices. First, an algebraic framework is used to solve the unbiasedness condition and second, a change of variable is introduced on the inputs of the system to reduce the...

We proceed from the view that linguistic variation must be examined from an aggregate perspective, i.e. from a perspective which encompasses as much of the variation between language varieties as possible rather than concentrating on single linguistic features. We review the motivation for this position in the rst section of the article, and then examine ways in which aggregate variation can be...

We study asymptotic distributions of the sums yn(x) = ∑n−1 k=0 ψ(x + kα) with respect to the Lebesgue measure, where α ∈ R−Q and where ψ is the 1-periodic function of bounded variation such that ψ(x) = 1 if x ∈ [0, 1/2[ and ψ(x) = −1 if x ∈ [1/2, 1[. For every α ∈ R − Q, we find a sequence (nj)j ⊂ N such that ynj/ √ j is asymptotically normally distributed. For n ≥ 1, let zn ∈ (ym)m≤n be such t...

The bilinear Generalized predictive controller is modified to account for unmodelled plant uncertainties and bounded disturbances. First, a generalized predictive control law is derived by means of minimizing a quadratic cost function and then modified by introducing an estimate of the modeling error as a feedback. The robustness results are derived by neither requiring a prior knowledge of the...

In joint work with C. Thiele, the author has shown that A. Calderón’s bilinear Hilbert transform extends to a bounded operator on certain products of L spaces. This article illustrates the method of proof by giving a complete proof of an inequality which is slightly weaker than the original conjecture of Calderón concerning this transform. 1991 Mathematics Subject Classification: 42A50

We provide alternative proofs of two recent Grothendieck theorems for jointly completely bounded bilinear forms, originally due to Pisier and Shlyakhtenko [PS02] and Haagerup and Musat [HM08]. Our proofs are elementary and are inspired by the so-called embezzlement states in quantum information theory. Moreover, our proofs lead to quantitative estimates.