Extended Chebyshev piecewise spaces characterised via weight functions

Piecewise Extended Chebyshev spaces: A numerical test for design

Given a number of Extended Chebyshev (EC) spaces on adjacent intervals, all of the same dimension, we join them via convenient connection matrices without increasing the dimension. The global space is called a Piecewise Extended Chebyshev (PEC) Space. In such a space one can count the total number of zeroes of any non-zero element, exactly as in each ECsection-space. When this number is bounded...

Rational Szego quadratures associated with Chebyshev weight functions

In this paper we characterize rational Szegő quadrature formulas associated with Chebyshev weight functions, by giving explicit expressions for the corresponding para-orthogonal rational functions and weights in the quadratures. As an application, we give characterizations for Szegő quadrature formulas associated with rational modifications of Chebyshev weight functions. Some numerical experime...

Good Banach Spaces for Piecewise Hyperbolic Maps via Interpolation

We introduce a weak transversality condition for piecewise C1+α and piecewise hyperbolic maps which admit a C1+α stable distribution. We show good bounds on the essential spectral radius of the associated transfer operators acting on classical anisotropic Sobolev spaces of Triebel-Lizorkin type. In many cases, we obtain a spectral gap from which we deduce the existence of finitely many physical...

Interpolation by Weak Chebyshev Spaces

We present two characterizations of Lagrange interpolation sets for weak Chebyshev spaces. The rst of them is valid for an arbitrary weak Chebyshev space U and is based on an analysis of the structure of zero sets of functions in U extending Stockenberg's theorem. The second one holds for all weak Chebyshev spaces that possess a locally linearly independent basis. x1. Introduction Let U denote ...

ε-weakly Chebyshev subspaces and quotient spaces