Synopsis
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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.
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Reseña del editor
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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.
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T(1) Theorem
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Taschenbuch. Condition: 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(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. 80 pp. Englisch. Seller Inventory # 9786131156915
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T(1) Theorem : Distribution (Mathematics), Kernel (Integral Operator)
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Taschenbuch. Condition: 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). 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. Seller Inventory # 9786131156915
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T(1) Theorem | Distribution (Mathematics), Kernel (Integral Operator)
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Taschenbuch. Condition: 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: preigu Print on Demand. Seller Inventory # 113278452
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T(1) Theorem
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Taschenbuch. Condition: 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. Seller Inventory # 9786131156915