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T(1) Theorem
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High Quality Content by WIKIPEDIA articles! In mathematics, the T(1) theorem, first proved by David & Journé (1984), describes when an operator T given by a kernel can be extended to a bounded linear operator on the Hilbert space L2(Rn). The name T(1) theorem refers to a condition on the distribution T(1), given by the operator T applied to the function 1. Suppose that T is a continuous operator from Schwartz functions on Rn to tempered distributions, so that T is given by a kernel K which is a distribution. Assume that the kernel is standard, which means that off the diagonal it is given by a function satisfying certain conditions. Then the T(1) theorem states that T can be extended to a bounded operator on the Hilbert space L2(Rn) if and only if the following conditions are satisfied: T(1) is of bounded mean oscillation (where T is extended to an operator on bounded smooth functions, such as 1). T (1) is of bounded mean oscillation, where T is the adjoint of T. T is weakly bounded, a weak condition that is easy to verify in practice.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131156915
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- EAN 9786131156915
- Format Fachbuch
- Titel T(1) Theorem
- Herausgeber Betascript Publishing
- Anzahl Seiten 80
- Genre Mathematik
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