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Some orthogonalities in approximation theory
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 20, Tome 314 (2004), pp. 83-123 Cet article a éte moissonné depuis la source Math-Net.Ru

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In approximation theory, a number of quantities are interrelated via orthogonal transformations. The revelation of these orthogonalities allows one to obtain useful relations and, in particular, to use known theorems on the Fourier coefficients. The paper considers this approach in application to the Fourier transforms of finite functions, to the best $L_2$-approximations, and to trigonometric polynomials with coefficients in a vector space. 
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A. S. Zhuk; V. V. Zhuk. Some orthogonalities in approximation theory. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 20, Tome 314 (2004), pp. 83-123. http://geodesic.mathdoc.fr/item/ZNSL_2004_314_a6/

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