Modern electronic devices such as cameras and computers use (among others) the
jpeg-format to store photographs. Millions of people employ such wavelet-based
technology every day. In sharp contrast to that, only a few thousand people on
the planet have a detailed understanding of the mathematics concerning the
C*-algebras O_n even though (as the book under review shows) there is a
strong relationship between the two.

This book entertains and educates the reader with a high-precision tour
connecting very current technological advances such as high-tech filters and
compression methods, classical mathematics such as wavelets and probability
theory and advanced, new mathematical methods such as non-commutative Hilbert
space operator algebra applications. This book distinguishes itself by placing
modern mathematics close to modern technology and by showing (again) that pure
mathematics is not necessarily only for mathematics' sake. The author Palle
E.T. Jorgensen is a world-class mathematician with a distinguished publication
record. This is a book that *every* student of mathematics should read in
order to be guided and motivated what courses to take, what other more basic
books to read, and what research to pursue. This is a book that computer
scientists, physicists and engineers should read. In my opinion, it could
spawn new innovation, maybe no patents, but benefits for all of mankind.

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