Analytic Pseudo-Differential Operators and their Applications

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.

Klappentext

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.