In mathematical analysis, the Schur test, named after German mathematician Issai Schur, is a bound on the operator norm of an integral operator in terms of its (see Schwartz kernel theorem). Here is one version. Let be two measurable spaces (such as ). Let be an integral operator with the non-negative Schwartz kernel , , : If there exist real functions and and numbers such that for almost all and for almost all , then extends to a continuous operator with the operator norm Such functions , are called the Schur test functions. In the original version, is a matrix and .
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| - Schur test (en)
- Тест Шура (ru)
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| - In mathematical analysis, the Schur test, named after German mathematician Issai Schur, is a bound on the operator norm of an integral operator in terms of its (see Schwartz kernel theorem). Here is one version. Let be two measurable spaces (such as ). Let be an integral operator with the non-negative Schwartz kernel , , : If there exist real functions and and numbers such that for almost all and for almost all , then extends to a continuous operator with the operator norm Such functions , are called the Schur test functions. In the original version, is a matrix and . (en)
- В функциональном анализе тест Шура (названный в честь математика Исая Шура) применяется для интегральных операторов с ядром, действующим . Такой тест позволяет дать оценку норме интегрального оператора, что позволяет делать вывод о его непрерывности. (ru)
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| - In mathematical analysis, the Schur test, named after German mathematician Issai Schur, is a bound on the operator norm of an integral operator in terms of its (see Schwartz kernel theorem). Here is one version. Let be two measurable spaces (such as ). Let be an integral operator with the non-negative Schwartz kernel , , : If there exist real functions and and numbers such that for almost all and for almost all , then extends to a continuous operator with the operator norm Such functions , are called the Schur test functions. In the original version, is a matrix and . (en)
- В функциональном анализе тест Шура (названный в честь математика Исая Шура) применяется для интегральных операторов с ядром, действующим . Такой тест позволяет дать оценку норме интегрального оператора, что позволяет делать вывод о его непрерывности. (ru)
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