Geodesic
Sobolev-orthogonal systems of functions and some of their applications
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 74 (2019) no. 4, pp. 659-733

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Systems of functions are considered which are associated with a given orthogonal system and are orthogonal with respect to an inner product of Sobolev type involving terms with masses concentrated at a point. Special attention is paid to such systems generated by classical orthogonal systems such as the cosine system, the Haar system, and the systems of Legendre, Jacobi, and Laguerre polynomials. The approximation properties of Fourier series in Sobolev-orthogonal systems are investigated in several cases. For (generally speaking, non-linear) systems of differential equations deep connections between Sobolev-orthogonal systems and the Cauchy problem are considered. Bibliography: 54 titles.
Keywords: Sobolev-orthogonal systems; Cauchy problem for a system of ordinary differential equations; systems generated by the Haar polynomials, the cosines, the Legendre
Mots-clés : Jacobi, Laguerre polynomials. 
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     author = {I. I. Sharapudinov},
     title = {Sobolev-orthogonal systems of functions and some of their applications},
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I. I. Sharapudinov. Sobolev-orthogonal systems of functions and some of their applications. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 74 (2019) no. 4, pp. 659-733. http://geodesic.mathdoc.fr/item/RM_2019_74_4_a2/