First self-contained, comprehensive treatment of the method of
dimensionality reducing expansion (DRE), a powerful technique for
changing a higher dimensional integration to a lower dimensional one
with or without remainder. DRE has broad connections to a number of
areas: numerical integration, pdes and Green's function, harmonic
analysis, numerical analysis and approximation theory. Exposition covers
the history of the subject and includes up-to-date new results, related
to many fields of current research such as boundary element methods for
solving pdes and wavelet analysis. Examples, comprehensive bibliography
and index included. Useful text or self-study resource for
graduate/advanced undergaduate students and researchers in pure and
applied mathematics, statistics, and physics.