- mathematics and statistics online
- Algebra of generalized functions (Shirokov) - Wikisource, the free online library
- Books by Mohamed Tarek Hussein
Differentiable Functions A2.
- Politics, Ideology, and Literary Discourse in Modern China: Theoretical Interventions and Cultural Critique.
- Ancient, Ancient.
- Account Options;
Fourier Transforms of Test Functions 1. The Case of Several Variables 1.
Analytic Functionals 1. Fourier Transforms of Functions in S 2.
mathematics and statistics online
Fourier Transforms of Generalized Functions. A Single Variable 2. Definition 2. Examples 2. Fourier Transforms of Analytic Functionals 3. Several Variables 3. Definitions 3. Fourier Transform of the Direct Product 3. Fourier Transforms and Differential Equations 4.
Introductory Remarks 4. Introductory Remarks on Differential Forms 1. Example: Derivation of Green's Theorem 1. Multiplet Layers 1. Generalized Functions Associated with Quadratic Forms 2. Elementary Solutions of Linear Differential Equations 2. Generalized Functions Associated with Bessel Functions 2.
- The Defender (Mills & Boon M&B)!
- Defining the derivative of a function and using derivative notation!
- Magari domani lo faccio (reNew) (Italian Edition)!
- Properties and Operations - 1st Edition?
- And the Bride Wore White Companion Guide: Seven Secrets to Sexual Purity!
Homogeneous Functions 3. Introduction 3. Generalized Homogeneous Functions of Degree —n 3. Generalized Homogeneous Functions of Degree —n — m 3. Reducible Singular Points 4. Generalized Functions of Complex Variables Bl. Homogeneous Functions of a Complex Variable B1. Generalized Functions of m Complex Variables B2.
Homogeneous Generalized Functions B2.
Associated Homogeneous Functions B2. The Residue of a Homogeneous Function B2. Homogeneous Generalized Functions of Degree —m,—m B2. Powered by. You are connected as.
Algebra of generalized functions (Shirokov) - Wikisource, the free online library
The product of a generalized function in and a function is defined by the equation. Here , and for ordinary functions in , the product coincides with the ordinary product of the functions and. However, this product operation cannot be extended to arbitrary generalized functions in such a way that it is associative and commutative, otherwise there would be the contradiction:.
In order to define the product of two generalized functions and , it is sufficient for them to possess, roughly speaking, the following properties: "non-regularity" of in a neighbourhood of any point must be compensated by corresponding "regularity" of , and conversely; for example, if see Support of a generalized function. A product can be defined in certain classes of generalized functions, but it may turn out not to be uniquely determined. In fact,. But on test functions for which ,.
Books by Mohamed Tarek Hussein
Hence it is natural to put if. Extending this functional to all test functions in , one obtains 4. The function does not belong to , but it defines regular generalized functions: in , , and in ,. They can be consistently extended to generalized functions in , for example, by taking the finite Hadamard part of the divergent integral renormalizing it.
View access options below. You previously purchased this article through ReadCube.
Institutional Login. Log in to Wiley Online Library. Purchase Instant Access. View Preview.
Learn more Check out. Citing Literature. Volume s , Issue 2 April Pages Related Information. Close Figure Viewer. Browse All Figures Return to Figure. Previous Figure Next Figure. Email or Customer ID.