In relation to Fourier-Pade approximation, Ed Sa¤ observed that Taylor and Lagrange interpolation projections satisfy the following property: P (f) P (g) 2 n =) P (f g) = P (f) P (g). We classify all projections that satisfy this property, thus answering a question of Sa¤. Some error formulas for approximation with the above mentioned projections are also produced. AMS Subject Classi…cation: 41...

A new conservative discrete ordinate method for nonlinear model kinetic equations is proposed. The conservation property with respect to the collision integral is achieved by satisfying at the discrete level approximation conditions used in deriving the model collision integrals. Additionally to the conservation property, the method ensures the correct approximation of the heat uxes. Numerical ...

We prove that the Lipschitz free spaces over certain types of discrete metric have Radon–Nikodým property. also show space a complete, locally compact has Schur or approximation property when

Exchange of patents between firms increasingly influence competition. Such cross-licensing deals have traditionally raised antitrust concerns, since they can be used to control market shares and prices, and create entry barriers. We argue that cross-licensing is a device to establish multimarket contact and is likely to raise antitrust concerns only in so far as multimarket contact does. Since ...

In this study, some existing results dealing with the weak approximation property of Banach spaces are considered for $p$-weak property. Also, an observation on bounded and $p$-bounded properties is given. Moreover, proof solution duality problem which exists in literature given a shorter way as alternative.

1. X-Z identity 2 1.1. Notation 2 1.2. XZ identities 3 1.3. Some estimates 4 2. Orthogonal Telescope Decomposition 6 2.1. Properties and Assumptions 6 2.2. Convergence 8 3. Approximation and Smoothing Property 8 3.1. High frequency 9 3.2. Approximation property 9 3.3. Smoothing property 9 3.4. Smoothing property of popular smoothers 10 3.5. Convergence 11 4. Stable Decomposition and Quasi-Ortho...