# Faber Systems and Their Use in Sampling, Discrepancy, Numerical Integration

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*Hans Triebel*

A publication of the European Mathematical Society

This book deals first with Haar bases, Faber bases and Faber frames
for weighted function spaces on the real line and the plane. It extends results
in the author's book, “Bases in Function Spaces, Sampling, Discrepancy,
Numerical Integration” (EMS, 2010), from unweighted spaces (preferably in
cubes) to weighted spaces.

The obtained assertions are used to study sampling and numerical integration
in weighted spaces on the real line and weighted spaces with dominating
mixed smoothness in the plane. A short chapter deals with the discrepancy for
spaces on intervals.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

#### Readership

Graduate students and mathematicians having a working knowledge of basic elements of function spaces and approximation theory.