Multivariate polynomials are a main tool in approximation. The
book begins with an introduction to the general theory by
presenting the most important facts on multivariate interpolation,
quadrature, orthogonal projections and their summation, all treated
under a constructive view, and embedded in the theory of positive
linear operators. On this background, the book gives the first
comprehensive introduction to the recently developped theory of
generalized hyperinterpolation. As an application, the book gives a
quick introduction to tomography. Several parts of the book are
based on rotation principles, which are presented in the beginning
of the book, together with all other basic facts needed.
General
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