Unboundedness of the Lipschitz Constants of Best Polynomial Approximation
نویسندگان
چکیده
منابع مشابه
A method to obtain the best uniform polynomial approximation for the family of rational function
In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...
متن کاملThe best uniform polynomial approximation of two classes of rational functions
In this paper we obtain the explicit form of the best uniform polynomial approximations out of Pn of two classes of rational functions using properties of Chebyshev polynomials. In this way we present some new theorems and lemmas. Some examples will be given to support the results.
متن کاملextensions of some polynomial inequalities to the polar derivative
توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی
15 صفحه اولBest constants for Lipschitz embeddings of metric spaces into c
We answer a question of Aharoni by showing that every separable metric space can be Lipschitz 2-embedded into c0 and this result is sharp; this improves earlier estimates of Aharoni, Assouad and Pelant. We use our methods to examine the best constant for Lipschitz embeddings of the classical `p-spaces into c0 and give other applications. We prove that if a Banach space embeds almost isometrical...
متن کاملThe Best Constants for Operator Lipschitz Functions on Schatten Classes
Suppose that f is a Lipschitz function on R with ‖f‖Lip ≤ 1. Let A be a bounded self-adjoint operator on a Hilbert space H. Let p ∈ (1,∞) and suppose that x ∈ B(H) is an operator such that the commutator [A, x] is contained in the Schatten class Sp. It is proved by the last two authors, that then also [f(A), x] ∈ Sp and there exists a constant Cp independent of x and f such that ‖[f(A), x]‖p ≤ ...
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: 2000
ISSN: 0021-9045
DOI: 10.1006/jath.2000.3492