منابع مشابه
Some 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 کاملSome Inequalities for Polynomials
Let pn(z) be a polynomial of degree n. Given that pn(z) has a zero on the circle \z\ = p(0 < p < oo) we estimate maxi , Ä>1 |/>„(z)| in terms of maxi:i , |/>„(z)|. We also consider some other related problems. It is well known (see [8, p. 346], or [6, vol. 1, p. 137, Problem III 269]) that if pn(z) = 2yt=oaAz/c 's a polynomial of degree « such that |p„(z)| â M for |z| Si 1, then at a point z ou...
متن کاملMARKOV- AND BERNSTEIN-TYPE INEQUALITIES FOR MÜNTZ POLYNOMIALS AND EXPONENTIAL SUMS IN Lp
The principal result of this paper is the following Markov-type inequality for Müntz polynomials. Theorem (Newman’s Inequality in Lp[a, b] for [a, b] ⊂ (0,∞)). Let Λ := (λj) ∞ j=0 be an increasing sequence of nonnegative real numbers. Suppose λ0 = 0 and there exists a δ > 0 so that λj ≥ δj for each j. Suppose 0 < a < b and 1 ≤ p ≤ ∞. Then there exists a constant c(a, b, δ) depending only on a, ...
متن کاملMarkov and Bernstein Inequalities in Lp for Some Weighted Algebraic and Trigonometric Polynomials
Let Qm,n (with m≤ n) denote the space of polynomials of degree 2m or less on (−∞,∞), weighted by (1 + x2)−n. The elements Qm,n are thus rational functions with denominator (1 + x2)m and numerator of degree at most 2m (if m = n, we can write, more briefly, Qn for Qn,n). The spaces Qm,n form a nested sequence as n increases and r = n−m is held to some given value of weighted polynomial spaces, wi...
متن کاملInequalities for Lorentz polynomials
We prove a few interesting inequalities for Lorentz polynomials. A highlight of this paper states that the Markov-type inequality max x∈[−1,1] |f (x)| ≤ n max x∈[−1,1] |f(x)| holds for all polynomials f of degree at most n with real coefficients for which f ′ has all its zeros outside the open unit disk. Equality holds only for f(x) := c((1± x) − 2n−1) with a constant 0 6= c ∈ R. This should be...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1988
ISSN: 0021-9045
DOI: 10.1016/0021-9045(88)90073-1