This book gives a new and direct approach into the theories of special functions with emphasis on spherical symmetry in Euclidean spaces of ar- bitrary dimensions. Essential parts may even be called elementary because of the chosen techniques. The central topic is the presentation of spherical harmonics in a theory of invariants of the orthogonal group. H. Weyl was one of the first to point out that spherical harmonics must be more than a fortunate guess to simplify numerical computations in mathematical physics. His opinion arose from his occupation with quan- tum mechanics and was supported...

Motivation The latest texts on linear systems for engineering students have begun incorpo- rating chapters on robust control using the state space approach to HOC control for linear finite dimensional time-invariant systems. While the pedagogical and computational advantages of this approach are not to be underestimated, there are, in my opinion, some disadvantages. Among these disadvantages is the narrow viewpoint that arises from the amputation of the finite dimensional time-invariant case from the much more general theory that had been developed using frequency domain methods. The...

The mathematical works of Fritz John whose deep and original ideas have had a great influence on the development of various fields in mathema tical analysis are made available with these volumes. His works are certainly well known to the experts, but knowledge of his contributions may not have spread as widely as it should have. For example, the concept of functions of bounded mean oscillations plays a central role in harmonic analysis today, but it is perhaps less known that this class of functions was introduced by John as early as 1961, motivated by his work in elasticity theory. With the...

The author would like to acknowledge his obligation to all his (;Olleagues and friends at the Institute of Mathematical Sciences of New York University for their stimulation and criticism which have contributed to the writing of this tract. The author also wishes to thank Aughtum S. Howard for permission to include results from her unpublished dissertation, Larkin Joyner for drawing the figures, Interscience Publishers for their cooperation and support, and particularly Lipman Bers, who suggested the publication in its present form. New Rochelle FRITZ JOHN September, 1955 v] CONTENTS...