We now consider the family of operators Tλ, λ ≥ 0, defined on Rn by T̂λ f (ξ) = mλ f̂ (ξ), where mλ(ξ) = (1− |ξ|)+. These are the Bochner-Riesz multipliers, which can be viewed as an attempt to smooth out the singularity of the disc multiplier to see if we can obtain boundedness on a wider range of Lp spaces. Note that when λ = 0 we obtain S1, and that as λ increases, the multiplier mλ becomes sm...

In this paper we give some characterizations of M. Hamana’s injective envelope I(A) of a C∗-algebra A in the setting of operator spaces and completely bounded maps. These characterizations lead to simplifications and generalizations of some known results concerning completely bounded projections onto C∗-algebras. We prove that I(A) is rigid for completely bounded A-module maps. This rigidity yi...

We present an efficient approach to solve resource allocation problems with a single resource, a convex separable objective function, a convex separable resource-usage constraint, and variables that are bounded below and above. Through a combination of function evaluations and median searches, information on whether or not the upperand lowerbounds are binding is obtained. Once this information ...

We investigate nonlinear programs that have a nonempty but possibly unbounded Lagrange multiplier set and that satisfy the quadraticgrowth condition. We show that such programs can be transformed, by relaxing the constraints and adding a linear penalty term to the objective function, into equivalent nonlinear programs that have diierentiable data and a bounded Lagrange multiplier set and that s...

We investigate nonlinear programs that have a nonempty but possibly unbounded Lagrange multiplier set and that satisfy the quadratic growth condition. We show that such programs can be transformed, by relaxing the constraints and adding a linear penalty term to the objective function, into equivalent nonlinear programs that have differentiable data and a bounded Lagrange multiplier set and that...

ABSTRACT. This paper presents the architecture of the MFIBVP real-time multiplier which is ideal to be used in real-time system application. The MFIBVP technique is a combination of the MSB–First computation, the Interval-Bounded Arithmetic and the Variable-Precision computation techniques. The MFIBVP computation guarantees the computation carried out will produce high accuracy from the early c...

We study the question whether characteristic functions of strictly convex compact sets with smooth boundaries in R are L × L → L bounded bilinear Fourier multiplier operators on R × R. When n ≥ 2 we answer this question in the negative outside the local L case, i.e., when 1/p + 1/q = 1/r and 2 ≤ p, q, r′ <∞ fails. Our proof is based on a suitable adaptation of the Kakeya type construction emplo...

A matlab toolbox has been developed that analyzes digital lter structures. After describing the digital lter structure in a SPICE-like format, the programs of this toolbox can map a digital lter structure into a state-space description, convert a state-space description to a z-domain transfer function, compute the maximum signal magnitude when input is bounded by unity, compute noise power at t...

Given integers i, j, k, L,M , we establish a new double bounded q−series identity from which the three parameter (i, j, k) key identity of Alladi-Andrews-Gordon for Göllnitz’s (big) theorem follows if L,M → ∞. When L = M , the identity yields a strong refinement of Göllnitz’s theorem with a bound on the parts given by L. This is the first time a bounded version of Göllnitz’s (big) theorem has b...