A Theorem on Polynomial-Star Approximation

Thomson’s Theorem on Mean Square Polynomial Approximation

In 1991, J. E. Thomson determined completely the structure of H2(μ), the closed subspace of L2(μ) that is spanned by the polynomials, whenever μ is a compactly supported measure in the complex plane. As a consequence he was able to show that if H2(μ) = L2(μ), then every function f ∈ H2(μ) admits an analytic extension to a fixed open set Ω, thereby confirming in this context a phenomenon noted e...

The Runge approximation theorem for generalized polynomial hulls

Where ||P ||K = sup{|P (z)| : z ∈ K}. It is known from the Runge approximation theorem that every function which is holomorphic in a neighborhood of compact sets K with K = K̂ can be approximated uniformly on K by analytic polynomials. Our aim here is to prove the same result in the more general situation when the rôle of K̂ is played by the generalized polynomial hull hq(K) introduced by Basener...

On the polynomial Lindenstrauss theorem

The Bishop-Phelps theorem [1] states that for any Banach space X, the set of norm attaining linear bounded functionals is dense in X ′, the dual space of X. Since then, the study of norm attaining functions has attracted the attention of many authors. Lindenstrauss showed in [2] that there is no Bishop-Phelps theorem for linear bounded operators. Nevertheless, he proved that the set of bounded ...

A Polynomial Time Approximation

In this paper we study the following problem: Given n strings s1; s2; : : : ; sn, each of length m, nd a substring ti of length L for each si, and a string s of length L, such that max n i=1 d(s; ti) is minimized, where d(;) is the Hamming distance. The problem was raised in 6] in an application of genetic drug target search and is a key open problem in many applications 7]. The authors of 6] s...

Lectures on multivariate polynomial approximation