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.

Inhalt
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.