I have often thought how wonderful it would have been if any of my grandparents, not to mention my great grandparents, had jotted down some of their thoughts, experiences and accumulated wisdom on paper for me to read, irrespective of how trivial or mind-blowing they may have been. I could have gleamed a glimpse as to who they were and how they thought, even though they died long before I was born in most cases. I really feel the void of not having known them. This book is an attempt to correct that omission and is written for the benefit of my kin still to come.
Forming functions of operators is a basic task of many areas of linear analysis and quantum physics. Weyl’s functional calculus, initially applied to the position and momentum operators of quantum mechanics, also makes sense for finite systems of selfadjoint operators. By using the Cauchy integral formula available from Clifford analysis, the book examines how functions of a finite collection of operators can be formed when the Weyl calculus is not defined. The technique is applied to the determination of the support of the fundamental solution of a symmetric hyperbolic system of partial differential equations and to proving the boundedness of the Cauchy integral operator on a Lipschitz surface.
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