Rational wavelets on the real line

Rational Wavelets on the Real Linea

Rational Wavelets on the Real Linea

Wavelets on Closed Subsets of the Real Line

We construct orthogonal and biorthogonal wavelets on a given closed subset of the real line. We also study wavelets satisfying certain types of boundary conditions. We introduce the concept of \wavelet prob-ing", which is closely related to our construction of wavelets. This technique allows us to very quickly perform a number of diierent numerical tasks associated with wavelets. x1. Introducti...

Orthogonal rational functions and quadrature on the real half line

In this paper we generalize the notion of orthogonal Laurent polynomials to orthogonal rational functions. Orthogonality is considered with respect to a measure on the positive real line. From this, Gauss-type quadrature formulas are derived and multipoint Padé approximants for the Stieltjes transform of the measure. Convergence of both the quadrature formula and the multipoint Padé approximant...

POINTWISE PSEUDO-METRIC ON THE L-REAL LINE

In this paper, a pointwise pseudo-metric function on the L-realline is constructed. It is proved that the topology induced by this pointwisepseudo-metric is the usual topology.