Geodesic
The extreme function of a~linear functional in the weighted Sobolev space
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 2 (2011), pp. 5-15

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The element of the uniformly convex space on which a functional reaches its norm is constructed. The result finds an application in the theory of cubature formulas where the error of numerical integration is represented by a linear functional and may be estimated via its norm. The norm of the error functional is expressed through such element which is called an extreme function.
Keywords: extreme function, weighted Sobolev space, linear compactly supported functional, integral representation of a functional, norm of a functional, norm of an extreme function. 
@article{VTGU_2011_2_a0,
     author = {I. V. Korytov},
     title = {The extreme function of a~linear functional in the weighted {Sobolev} space},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {5--15},
     publisher = {mathdoc},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2011_2_a0/}
}
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I. V. Korytov. The extreme function of a~linear functional in the weighted Sobolev space. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 2 (2011), pp. 5-15. http://geodesic.mathdoc.fr/item/VTGU_2011_2_a0/