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About fifty years aga S. G. Mikhlin, in solving the regularization problem for two-dimensional singular integral operators 56], assigned to each such operator a func- tion which he called a symbol, and showed that regularization is possible if the infimum of the modulus of the symbol is positive. Later, the notion of a symbol was extended to multidimensional singular integral operators (of arbitrary dimension) 57, 58, 21, 22]. Subsequently, the synthesis of singular integral, and differential operators 2, 8, 9]led to the theory of pseudodifferential operators 17, 35] (see also ...

All the important classical examples of traces and determinants sugges, Ruston and Grothendieck are exhibited. In particular, the determinants which were first introduced in their investigations of infinite systems of li near equations stemmingfrom problems in celestial mechanics are studie d. Most of FredholmFs seminal results are presented in this book by th e editorsf own means. Formulas for traces and determinants in a Hilber t space setting are readily derived, again. Also investigated are gene ralizations to Banach spaces. Furthermore, a large part of this book i s devoted to...