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Approximation Theory and Harmonic Analysis on Spheres and Balls Förderungs- und Betriebs GmbH represented an i nternat iThis monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part