Approximation by Polynomials with Restricted Zeros
نویسندگان
چکیده
منابع مشابه
On the Zeros of Polynomials with Restricted Coefficients
It is proved that a polynomial p of the form
متن کاملSome compact generalization of inequalities for polynomials with prescribed zeros
Let $p(z)=z^s h(z)$ where $h(z)$ is a polynomial of degree at most $n-s$ having all its zeros in $|z|geq k$ or in $|z|leq k$. In this paper we obtain some new results about the dependence of $|p(Rz)|$ on $|p(rz)| $ for $r^2leq rRleq k^2$, $k^2 leq rRleq R^2$ and for $Rleq r leq k$. Our results refine and generalize certain well-known polynomial inequalities.
متن کاملRemez-, Nikolskii-, and Markov-Type Inequalities for Generalized Nonnegative Polynomials with Restricted Zeros
Generalized nonnegative polynomials were studied in a sequence of recent papers [4], [6], [7], [8], and [9]. A number of well-known inequalities in approximation theory were extended to them, by utilizing the generalized degree in place of the ordinary one. Our motivation was to find tools to examine systems of orthogonal polynomials simultaneously, associated with generalized Jacobi, or at lea...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1994
ISSN: 0021-9045
DOI: 10.1006/jath.1994.1116