منابع مشابه
A Finiteness Property for Preperiodic Points of Chebyshev Polynomials
Let K be a number field with algebraic closure K, let S be a finite set of places of K containing the archimedean places, and let φ be a Chebyshev polynomial. We prove that if α ∈ K is not preperiodic, then there are only finitely many preperiodic points β ∈ K which are S-integral with respect to α.
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We define a class of multivariate Laurent polynomials closely related to Chebyshev polynomials and prove the simple but somewhat surprising (in view of the fact that the signs of the coefficients of the Chebyshev polynomials themselves alternate) result that their coefficients are non-negative. As a corollary we find that Tn(c cos θ) and Un(c cos θ) are positive definite functions. We further s...
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We study several classes of polynomials, which are related to the Chebyshev, Morgan-Voyce, Horadam and Jacobsthal polynomials. Thus, we unify some of well-known results.
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The mth Chebyshev polynomial of a square matrix A is the monic polynomial that minimizes the matrix 2-norm of p(A) over all monic polynomials p(z) of degree m. This polynomial is uniquely defined if m is less than the degree of the minimal polynomial of A. We study general properties of Chebyshev polynomials of matrices, which in some cases turn out to be generalizations of well known propertie...
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We are concerned with the problem of minimizing the supremum norm on [0, 1] of a nonzero polynomial of degree at most n with integer coefficients. We use the structure of such polynomials to derive an efficient algorithm for computing them. We give a table of these polynomials for degree up to 75 and use a value from this table to answer an open problem due to P. Borwein and T. Erdélyi and impr...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1974
ISSN: 0021-9045
DOI: 10.1016/0021-9045(74)90085-9