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A simple model for a symmetrical theory of generalized functions: I. Definition of singular generalized functions

โœ Scribed by J.J. Lodder

Publisher
Elsevier Science
Year
1982
Tongue
English
Weight
673 KB
Volume
116
Category
Article
ISSN
0378-4371

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โœฆ Synopsis

A new theory of generalized functions, which is more suitable for physical applications than distribution theory, is developed. The necessary definitions are given and the scalar product is defined.

๐Ÿ“œ SIMILAR VOLUMES

A simple model for a symmetrical theory
A simple model for a symmetrical theory of generalized functions: V. Some applications
โœ J.J. Lodder ๐Ÿ“‚ Article ๐Ÿ“… 1982 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 331 KB

The theory of generalized functions is shown to eliminate ambiguities in products which are unavoidable in distribution theory. The physical examples are the velocity of shock waves and the It&Stratonovich dilemma.

A Global Theory of Algebras of Generaliz
A Global Theory of Algebras of Generalized Functions
โœ M. Grosser; M. Kunzinger; R. Steinbauer; J.A. Vickers ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 206 KB

We present a geometric approach to defining an algebra G ห†(M) (the Colombeau algebra) of generalized functions on a smooth manifold M containing the space DOE(M) of distributions on M. Based on differential calculus in convenient vector spaces we achieve an intrinsic construction of G ห†(M). G ห†(M) i

Toward a Unified Theory of Generalized F
Toward a Unified Theory of Generalized Functions: Convergence
โœ Piotr Mikusiล„ski; Michael D. Taylor ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 758 KB

Generalized functions are usually treated as bounded linear functionals on spaces of test functions. Here they are considered as objects which "convolute" with test functions and satisfy a certain associativity condition. In this setting simple definitions are given for convergence of sequences of t