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Multi-dimensional polynomial inequal...

Fontes, Natacha.

Multi-dimensional polynomial inequalities: Norms of interpolation operators.

紀錄類型:	書目-電子資源 : 單行本
正題名/作者:	Multi-dimensional polynomial inequalities: Norms of interpolation operators./
作者:	Fontes, Natacha.
面頁冊數:	63 p.
附註:	Source: Dissertation Abstracts International, Volume: 65-08, Section: B, page: 4053.
Contained By:	Dissertation Abstracts International65-08B.
標題:	Mathematics. -
電子資源:	Download fulltext (下載全文)
ISBN:	0496000705

Multi-dimensional polynomial inequalities: Norms of interpolation operators.
Fontes, Natacha.

Multi-dimensional polynomial inequalities: Norms of interpolation operators. - 63 p.

Source: Dissertation Abstracts International, Volume: 65-08, Section: B, page: 4053.

Thesis (Ph.D.)--Kent State University, 2004.

In this dissertation we discuss various topics in approximation theory, including multi-dimensional polynomial inequalities and extremum problems in the Hardy space, Hinfinity (D), consisting of all functions which are analytic and bounded in the open unit disk D.

ISBN: 0496000705Subjects--Topical Terms:

146772
Mathematics.

Multi-dimensional polynomial inequalities: Norms of interpolation operators.
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245 1 0 $a Multi-dimensional polynomial inequalities: Norms of interpolation operators.
300 $a 63 p.
500 $a Source: Dissertation Abstracts International, Volume: 65-08, Section: B, page: 4053.
500 $a Directors: Alfred Cavaretta; Laura Smithies.
502 $a Thesis (Ph.D.)--Kent State University, 2004.
520 $a In this dissertation we discuss various topics in approximation theory, including multi-dimensional polynomial inequalities and extremum problems in the Hardy space, Hinfinity (D), consisting of all functions which are analytic and bounded in the open unit disk D.
520 $a We prove a two-dimensional version of Turan's first main theorem, along with some applications. Specifically, we consider the power sum S(i, j) = l=1n k=1m bklwkizl j, for bkl, wk, zl ∈ C , and provide an upper bound for |S(0, 0)| in terms of the maximum of |S| over the lattice of points of a region in R2 which is a given distance from the origin.
520 $a We also provide a multi-dimensional version of Nazarov's extension of Turan's lemma---a theorem in which the uniform norm of a complex valued polynomial p defined on the unit circle T is compared with the uniform norm of p on any measurable subset of T . If we let Tn := T x �� x T represent the distinguished boundary of the polydisk D n := D x �� x D for some n ∈ N then, as in the one-dimensional case, the constant which relates the uniform norm of p on Tn to the uniform norm of p on any measurable subset of Tn depends on the order, i.e., the number of non-zero coefficients, of p and the measure of the set E.
520 $a The second topic of this dissertation concerns calculating the norms of various Lagrange interpolation functionals acting on the Hardy space Hinfinity (D). For example, we calculate the norm of Ln-1(�;zeta), where Ln-1(�;zeta) represents the Lagrange interpolation polynomial of degree n - 1, evaluated at some complex number zeta, and defined by interpolating functions in Hinfinity (D) at the zeros of zn - rn, for various values of n and zeta. We assume that 0 < r < 1 and that |zeta| > 1. We also calculate the norm of L1(�;zeta) in the case that L1(�;zeta) is defined by interpolating functions in Hinfinity (D) at two arbitrary fixed values in (-1,1), as opposed to the symmetrical values r and - r.
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790 1 0 $a Cavaretta, Alfred, $e advisor
790 1 0 $a Smithies, Laura, $e advisor
790 $a 0101
791 $a Ph.D.
792 $a 2004
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3141574 $z Download fulltext (下載全文)