Geodesic
Construction of polynomials of a~special kind and examples of their application in the theory of power series and in the wavelet theory
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2011), pp. 24-38

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In this paper we construct polynomials of a special type. We consider examples of their application for studying the convergence of special power series, for determining the upper and lower Riesz bounds for a basis consisting of $B$-splines, and for studying the convergence of a sequence of Battle–Lemarié scaling functions.
Keywords: functional series, $B$-splines, Riesz basis, Battle–Lemarié scaling function, Shennon–Kotel'nikov function. 
@article{IVM_2011_1_a2,
     author = {E. V. Mishchenko},
     title = {Construction of polynomials of a~special kind and examples of their application in the theory of power series and in the wavelet theory},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {24--38},
     publisher = {mathdoc},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_1_a2/}
}
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E. V. Mishchenko. Construction of polynomials of a~special kind and examples of their application in the theory of power series and in the wavelet theory. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2011), pp. 24-38. http://geodesic.mathdoc.fr/item/IVM_2011_1_a2/