Generalized Functions In Mathematical Physics

Argumento de Generalized Functions In Mathematical Physics

1. Basic and Generalized Functions
2. Differentiation of Generalized Functions
3. Direct Product of Generalized Functions
4. The Convolution of Generalized Functions
5. Generalized Functions of Slow Growth

Chapter II. Integral Transformations of Generalized Functions

6. The Fourier Transform of Generalized Function of Slow Growth
7. Fourier Series of Periodic Generalized Functions
8. Positive Definite Generalized Functions
9. The Laplace Transform of Generalized Functions of Slow Growth
10. The Cauchy Kernel and the Transforms of Cauchy-Bochner and Hilbert
11. Poisson Kernel and Poisson Transform
12. Algebras of Holomorphic Functions
13. Equations in Convolution Algebras

Chapter III. Some Applications in Mathematical Physics

14. Differential Operators With Constatne Coefficients
15. Cauchy Problem
16. Holomorphic Functions With Nonnegative Imaginary Part in Tc
17. Holomorphic Functions With Nonnegative Imaginary Part in Tn
18. Positive Real Matrix Functions in Tc
19. Linear Passive Systems
20. Abstract Scattring Operator