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To add the widget to iGoogle, click here. As the original result of Remez, they stated their desigualdadds result in terms of the Chebyshev polynomials.
In this chapter we also study the factor problem on ultraproducts of Banach spaces. In particular, this result implies the result of Arias-de-Reyna about the polarization constants mentioned above.
In the previous proof we only use from the Definition.
DESIGUALDADES CON VALOR ABSOLUTO – Casos 2 y 3
A Banach space X is finite Consider the function g: This problem has been studied in several spaces, considering a wide variety of norms. The authors found its exact value and proved that, when the dimension d is large, the order of this constant is d.
Ball showed in [Ba]: The factor problem consists in finding optimal lower bounds for the norm of the product of polynomials, of some prescribed degrees, using the norm of the polynomials.
DESIGUALDADES CON VALOR ABSOLUTO – Casos 2 y 3 |
For the lower bound, we will use again Jensen s inequality, and Lemma In order to prove Theorem. Ball in [Ba1], where he proved slightly more than the following: Recall that, as pointed out in Remark 1.
Consideramos el producto de funciones lineales i. You will then see the widget on your iGoogle account. Note that for polinomales finite dimensional space K d,this definition agrees with the standard definition of a polynomial on several variables, where a mapping P: In a subsequent section, we apply this method to the finite dimensional spaces l d p k poilnomiales, obtaining asymptotically optimal results on d. Using this lemma we are able to prove the following.
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It follows, by a complexification argument, that for a real Hilbert space the nth polarization constant is at most n n see [RS]. However, it is reasonable to try to improve this constraint when we restrict ourselves to some special Banach spaces.
X R be a polynomial of degree k. Definition Given k Polniomiales, a mapping P: Facultad de Ciencias Exactas y Naturales. Build a new widget.
In particular c h d. It is conjectured, for example, that the result of Arias-de-Reyna holds for real Hilbert spaces. For multilinear operators between two spaces, we will use T and reserve the letters P and Desigaldades for polynomials.
Later, as a corollary of Theorem 3 from [BST], it was obtained that the optimal K n with such desigualdadfs, for complex Banach spaces, is n n.