Best uniform approximation with Hermite-Birkhoff interpolatory side conditions

Hermite-interpolatory subdivision schemes

Stationary interpolatory subdivision schemes for Hermite data that consist of function values and first derivatives are examined. A general class of Hermite-interpolatory subdivision schemes is proposed, and some of its basic properties are stated. The goal is to characterise and construct certain classes of nonlinear (and linear) Hermite schemes. For linear Hermite subdivision, smoothness cond...

Uniform Birkhoff

We show that pseudovarieties of finitely generated algebras, i.e., classes C of finitely generated algebras closed under finite products, homomorphic images, and subalgebras, can be described via a uniform structure UC on the free algebra for C: the members of C then are precisely those finitely generated algebras A for which the natural mapping from the free algebra onto the term clone of A is...

Approximation with Interpolatory Constraints

Given a triangular array of points on [−1, 1] satisfying certain minimal separation conditions, a classical theorem of Szabados asserts the existence of polynomial operators that provide interpolation at these points as well as a near-optimal degree of approximation for arbitrary continuous functions on the interval. This paper provides a simple, functional-analytic proof of this fact. This abs...

Best Uniform Approximation 3 Theorem 1

We present a Chebyshev-type characterization for the best uniform approximations of periodic continuous functions by functions of the class M = ff(x) : f(x) = Z 2 0 K(x; y)h(y) dy; jh(y)j 1 a: e:; y 2 0; 2)g; where K(x; y) is a strictly cyclic variation diminishing kernel. x1 Introduction Let W r 1 a; b] be the Sobolev class of functions in C r?1 a; b] whose (r?1)st derivative is absolutely con...

Fourier transform of Hermite interpolatory subdivision schemes