In this paper we generalize the Hill-Moylan-Willems framework for dissipative systems to accommodate L∞ criteria, and a mixture of L∞ and integral criteria. The generalized dissipation property is completely characterized in terms of a partial differential inequality, interpreted in the viscosity sense. These results are then applied to derive a state feedback synthesis procedure using a minima...

In this paper, we prove that for l = 1 or 2 the rate of best l-monotone polynomial approximation in the Lp norm (1 ≤ p ≤ ∞) weighted by the Jacobi weight wα ,β(x) ∶= (1 + x)α(1 − x)β with α, β > −1/p if p <∞, or α, β ≥ 0 if p =∞, is bounded by an appropriate (l + 1)-st modulus of smoothness with the same weight, and that this rate cannot be bounded by the (l+2)-ndmodulus. Related results on con...

Uncertainty principles for generating systems {en} ∞ n=1 ⊂ L (R) are proven and quantify the interplay between l(N) coefficient stability properties and time-frequency localization with respect to |t| power weight dispersions. As a sample result, it is proven that there does not exist a unit-norm Schauder basis nor a frame {en} ∞ n=1 for L (R) such that the two dispersion sequences ∆(en), ∆(ên)...

For f ∈ S(R), we consider the Bochner-Riesz operator R of index δ > 0 defined by R̂δf(ξ) = (1− |ξ|)+ f̂(ξ). Then we prove the Bochner-Riesz conjecture which states that if δ > max{d|1/p − 1/2| − 1/2, 0} and p > 1 then R is a bounded operator from L(R) into L(R); moreover, if δ(p) = d(1/p − 1/2) − 1/2 and 1 < p < 2d/(d + 1), then Rδ(p) is a bounded operator from L(R) into L(R).

‎Let $X,Y$ be normed spaces with $L(X,Y)$ the space of continuous‎ ‎linear operators from $X$ into $Y$‎. ‎If ${T_{j}}$ is a sequence in $L(X,Y)$,‎ ‎the (bounded) multiplier space for the series $sum T_{j}$ is defined to be‎ [ ‎M^{infty}(sum T_{j})={{x_{j}}in l^{infty}(X):sum_{j=1}^{infty}%‎ ‎T_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $S:M^{infty}(sum T_{j})rightarrow Y$ associat...

where dσr is the normalized surface measure on r S . It is easy to see that M is not bounded on L (see Example 1.1 below). A well-known result of Bourgain [1] asserts that M is bounded on L for 2 < p ≤ ∞. We will consider the question of boundedness of M and Mδ from L to L. Unless stated to the contrary, we will be dealing only with functions defined on R. Absolute constants will be denoted by ...

Innovative multi-channel synthetic aperture radar (SAR) concepts enable high-resolution wide-swath imaging, but the antenna length typically restricts the achievable swath width. This limitation can be overcome by a novel technique which is based on a single azimuth channel but operates the system with a continuously varied pulse repetition frequency (PRF) by this allowing in principle for arbi...

The notion of generalized locally bounded $I$-topological vectorspaces is introduced. Some of their important properties arestudied. The relationship between this kind of spaces and thelocally bounded $I$-topological vector spaces introduced by Wu andFang [Boundedness and locally bounded fuzzy topological vectorspaces, Fuzzy Math. 5 (4) (1985) 87$-$94] is discussed. Moreover, wealso use the fam...

We study divisibilities between bounded holomorphic quasi-inner functions in H∞ and operator-valued bounded holomorphic quasi-inner functions in H∞(Ω, L(K)) where Ω is a bounded finitely connected region. Furthermore, we characterize these divisibilities by using rationally-invariant subspaces.

Motivated by strong Karp-Lipton collapse results in bounded arithmetic, Cook and Kraj́ıček [1] have recently introduced the notion of propositional proof systems with advice. In this paper we investigate the following question: Given a language L, do there exist polynomially bounded proof systems with advice for L? Depending on the complexity of the underlying language L and the amount and type ...