Schur Test
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High Quality Content by WIKIPEDIA articles! n mathematical analysis, the Schur Test (named after German mathematician Issai Schur) is the name for the bound on the L^2to L^2 operator norm of an integral operator in terms of its Schwartz kernel (see Schwartz kernel theorem). Here is one version. Let X and Y be two measurable spaces (such as mathbb{R}^n). Let T be an integral operator with the non-negative Schwartz kernel K(x,y), xin X, yin Y: T: L^2(Y)to L^2(X), qquad T f(x)=int_Y K(x,y)f(y),dy.

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High Quality Content by WIKIPEDIA articles! n mathematical analysis, the Schur Test (named after German mathematician Issai Schur) is the name for the bound on the L^2to L^2 operator norm of an integral operator in terms of its Schwartz kernel (see Schwartz kernel theorem). Here is one version. Let X and Y be two measurable spaces (such as mathbb{R}^n). Let T be an integral operator with the non-negative Schwartz kernel K(x,y), xin X, yin Y: T: L^2(Y)to L^2(X), qquad T f(x)=int_Y K(x,y)f(y),dy.