9786131156915 - t(1) theorem: distribution (mathematics), kernel (integral operator) (4 Ergebnisse)
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Taschenbuch. Zustand: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - 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). T…he 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.
Verlag: Omniscriptum Mär 2026, 2026
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Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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(R…n). 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. 80 pp. Englisch.
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Taschenbuch. Zustand: Neu. T(1) Theorem | Distribution (Mathematics), Kernel (Integral Operator) | Lambert M. Surhone (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786131156915 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: pr…eigu Print on Demand.
Verlag: Omniscriptum Mär 2026, 2026
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Taschenbuch. Zustand: Neu. This item is printed on demand - Print on Demand Titel. Neuware -High Quality Content by WIKIPEDIA articles! In mathematics, the T(1)theorem, first proved by David & Journé (1984), describes when anoperator T given by a kernel can be extended to a bounded linearoperator on the Hilbert space L2(Rn). The… name T(1) theorem refers to acondition on the distribution T(1), given by the operator T applied tothe function 1. Suppose that T is a continuous operator from Schwartzfunctions on Rn to tempered distributions, so that T is given by akernel K which is a distribution. Assume that the kernel is standardwhich means that off the diagonal it is given by a function satisfyingcertain conditions. Then the T(1) theorem states that T can be extendedto a bounded operator on the Hilbert space L2(Rn) if and only if thefollowing conditions are satisfied: \* T(1) is of bounded meanoscillation (where T is extended to an operator on bounded smoothfunctions, 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 iseasy to verify in practice.VDM Verlag, Dudweiler Landstraße 99, 66123 Saarbrücken 80 pp. Englisch.
