Publications de l'Institut Mathématique, Nouvelle Série Vol. 97(111), pp. 57–67 (2015) 

ON LINEAR COMBINATIONS OF CHEBYSHEV POLYNOMIALSDragan StankovKatedra Matematike RGFa, University of Belgrade, Belgrade, SerbiaAbstract: We investigate an infinite sequence of polynomials of the form: $$ a_0T_n(x)+a_1T_{n1}(x)+\dots+a_mT_{nm}(x) $$ where $(a_0,a_1,\ldots,a_m)$ is a fixed $m$tuple of real numbers, $a_0,a_m\neq0$, $T_i(x)$ are Chebyshev polynomials of the first kind, $n=m,m+1,m+2,\ldots$ Here we analyze the structure of the set of zeros of such polynomial, depending on $A$ and its limit points when $n$ tends to infinity. Also the expression of envelope of the polynomial is given. An application in number theory, more precise, in the theory of Pisot and Salem numbers is presented. Keywords: Chebyshev polynomials, envelope, Pisot numbers, Salem numbers Classification (MSC2000): 11B83; 11R09;12D10 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 16 Apr 2015. This page was last modified: 21 Apr 2015.
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