Geodesic
Supremum Norms for 2-Homogeneous Polynomials on Circle Sectors
Journal of convex analysis, Tome 21 (2014) no. 3, pp. 745-764.

Voir la notice de l'article provenant de la source Heldermann Verlag

We consider the Banach space of two homogeneous polynomials endowed with the supremum norm $\|\cdot\|_{D(\beta)}$ over circle sectors $D(\beta)$ of angle $\beta$ for several values of $\beta\in[0,2\pi]$. We provide an explicit formula for $\|\cdot\|_{D(\beta)}$, a full description of the extreme points of the corresponding unit balls, and a parametrization and a plot of their unit spheres. This work is an extension of a series of papers on the same topic published in the last decade and it has a number of applications to obtain polynomial-type inequalities.
Classification : 46G25, 46B28, 41A44
Mots-clés : Bernstein and Markov inequalities, unconditional constants, polarizations constants, polynomial inequalities, homogeneous polynomials, extreme points 
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     author = {G. A. Mu\~noz-Fern\'andez and D. Pellegrino and J. B. Seoane-Sep\'ulveda and A. Weber},
     title = {Supremum {Norms} for {2-Homogeneous} {Polynomials} on {Circle} {Sectors}},
     journal = {Journal of convex analysis},
     pages = {745--764},
     publisher = {mathdoc},
     volume = {21},
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     year = {2014},
     url = {http://geodesic.mathdoc.fr/item/JCA_2014_21_3_JCA_2014_21_3_a8/}
}
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G. A. Muñoz-Fernández; D. Pellegrino; J. B. Seoane-Sepúlveda; A. Weber. Supremum Norms for 2-Homogeneous Polynomials on Circle Sectors. Journal of convex analysis, Tome 21 (2014) no. 3, pp. 745-764. http://geodesic.mathdoc.fr/item/JCA_2014_21_3_JCA_2014_21_3_a8/