Multivariate integration has been a fundamental subject in
mathematics, with broad connections to a number of areas: numerical
analysis, approximation theory, partial differential equations,
integral equations, harmonic analysis, etc. In this work the
exposition focuses primarily on a powerful tool that has become
especially important in our computerized age, namely,
dimensionality reducing expansion (DRE). The method of DRE is a
technique for changing a higher dimensional integration to a lower
dimensional one with or without remainder. To date, there is no
comprehensive treatment of this subject in monograph or textbook
form.
Key features of this self-contained monograph include:
* fine exposition covering the history of the subject
* up-to-date new results, related to many fields of current
research such as boundary element methods for solving PDEs and
wavelet analysis
* presentation of DRE techniques using a broad array of
examples
* good balance between theory and application
* coverage of such related topics as boundary type quadratures
and asymptotic expansions of oscillatory integrals
* excellent and comprehensive bibliography and index
This work will appeal to a broad audience of students and
researchers in pure and applied mathematics, statistics, and
physics, and can be used in a graduate/advanced undergraduate
course or as a standard reference text.
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