# Bases in Function Spaces, Sampling, Discrepancy, Numerical Integration

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*Hans Triebel*

A publication of the European Mathematical Society

The first chapters of this book deal with Haar bases, Faber bases and
some spline bases for function spaces in Euclidean \(n\)-space and
\(n\)-cubes. These are used in the subsequent chapters to study sampling
and numerical integration preferably in spaces with dominating mixed
smoothness. The subject of the last chapter is the symbiotic relationship
between numerical integration and discrepancy, measuring the deviation of sets
of points from uniformity.

This book is addressed to graduate students and mathematicians who have a
working knowledge of basic elements of function spaces and approximation
theory and who are interested in the subtle interplay between function spaces,
complexity theory and number theory (discrepancy).

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

#### Readership

Graduate students and research mathematicians interested in complexity theory and number theory.