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Unconditional constants and polynomial inequalities

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Grecu, B.C. y Muñoz-Fernández, Gustavo A. y Seoane-Sepúlveda, Juan B. (2009) Unconditional constants and polynomial inequalities. Journal of Approximation Theory, 161 (2). pp. 706-722. ISSN 0021-9045

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URL Oficial: http://www.sciencedirect.com/science/article/pii/S002190450800258X


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If P is a polynomial on R of degree at most n, given by P(x) = Sigma(alpha is an element of Nm,vertical bar alpha vertical bar <= n) a(alpha)x(alpha), and P(n)(R(m)) is the space of such polynomials, then we define the polynomial vertical bar P vertical bar by vertical bar P vertical bar(x) = Sigma(alpha is an element of Nm,vertical bar alpha vertical bar <= n) vertical bar a(alpha vertical bar)x(alpha). Now if B subset of R(m) is a convex set, we define the norm parallel to P parallel to(B) := sup{vertical bar(x)vertical bar : x is an element of B} on P(n)(R(m)), and then we investigate the inequality vertical bar vertical bar vertical bar P vertical bar vertical bar vertical bar(B) <= C(B)vertical bar vertical bar vertical bar P vertical bar vertical bar vertical bar(B), providing sharp estimates on C(B) for some specific spaces of polynomials. These C(B)'s happen to be the unconditional constants of the canonical bases of the considered spaces.


Tipo de documento:Artículo
Palabras clave:Unconditional constant; Polynomial inequalities; Trinomials; Homogeneous polynomials; Extreme points
Materias:Ciencias > Matemáticas > Análisis funcional y teoría de operadores
Código ID:16967
Depositado:05 Nov 2012 11:28
Última Modificación:28 Nov 2016 09:32

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