One service mathematics has rendered the 'Et moi, . . . , si j'avait su comment en revenir, je n'y serais point aIle:' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics . . . '; 'One service logic has rendered com puter science . . .'; 'One service category theory has rendered mathematics . . . '. All arguably true. And all statements obtainable this way form part of the raison d'elre of this series.
Inhaltsverzeichnis
I. PD-Operators with Complex Arguments. - 1. PD-Operators with Constant Analytic Symbols. - 2. Fourier Transformation of Arbitrary Analytic Functions. Complex Fourier Method. - 3. PD-Equations whose Symbols are Formal Series. - II. The Cauchy Problem in the Complex Domain. - 4. Cauchy-Kovalevskaya Theory in Spaces of Analytic Functions with Pole-type Singularities. - 5. Exponential theory of the Cauchy problem. - 6. PD-Operators with Variable Analytic Symbols. - III. PD-Operators with Real Arguments. - 7. Spaces of Test Functions and Distributions. - 8. Analytic PD-operators with Real Arguments. Applications. - References. - Author Index. - Index of Basic Formulae.
