Methods of the Theory of Generalized Functions

Vladimirov, V. S.

• Generalized Functions and Their Properties. Test and Generalized Functions. Differentiation of Generalized Functions. Direct Product of Generalized Functions. The Convolution of Generalized Functions. Tempered Generalized Functions. Integral Transformations of Generalized Functions. The Fourier Transform of Tempered Generalized Functions. Fourier Series of Periodic Generalized Functions. Positive Definite Generalized Functions. The Laplace Transform of Tempered Generalized Functions. The Cauchy Kernel and the Transforms of Cauchy-Bochner and Hilbert. Poisson Kernel and Poisson Transform. Algebras of Holomorphic Functions. Equations in Convolution Algebras. Tauberian Theorems for Generalized Functions. Some Applications in Mathematical Physics. Differential Operators with Constant Coefficients. The Cauchy Problem. Holomorphic Functions with Nonnegative Imaginary Part in T^Oc. Holomorphic Functions with Nonnegative Imaginary Part in T^On. Positive Real Matrix Functions in T^Oc. Linear Passive Systems. Abstract Scattering Operator.