Schwartz Kernel Theorem
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High Quality Content by WIKIPEDIA articles! In mathematics, the Schwartz kernel theorem is a foundational result in the theory of generalized functions, published by Laurent Schwartz in 1952. It states, in broad terms, that the generalized functions introduced by Schwartz himself (Schwartz distributions) have a two-variable theory that includes all reasonable bilinear forms on the space D of test functions. The space D itself consists of smooth functions of compact support. The traditional kernel functions K(x,y) of two variables of the theory of integral operators having been expanded in scope to include their generalized function analogues, which are allowed to be more singular in a serious way, a large class of operators from D to its dual space D of distributions can be constructed. The point of the theorem is to assert that the extended class of operators can be characterised abstractly, as containing all operators subject to a minimum continuity condition. A bilinear form on D arises by pairing the image distribution with a test function.
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GarantieWeitere Informationen
- Allgemeine Informationen
- GTIN 09786131173394
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- EAN 9786131173394
- Format Fachbuch
- Titel Schwartz Kernel Theorem
- Herausgeber Betascript Publishing
- Anzahl Seiten 116
- Genre Mathematik
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