Muñoz-Fernández, Gustavo Adolfo and Seoane Sepúlveda, Juan Benigno
(2008)
*Geometry of Banach spaces of trinomials.*
Journal of Mathematical Analysis and Applications, 340
(2).
pp. 1069-1087.
ISSN 0022-247X

PDF
Restricted to Repository staff only until 2020. 790kB |

Official URL: http://www.sciencedirect.com/science/article/pii/S0022247X07011237

## Abstract

For each pair of numbers m, n epsilon N with m > n, we consider the norm on R-3 given by parallel to(a, b, c)parallel to m,n = sup{vertical bar ax(m) +bx(n) +C vertical bar: x epsilon [-1, 1]} for every (a, b, c) epsilon R-3. We investigate some geometrical properties of these norms. We provide an explicit formula for parallel to center dot parallel to m,n, a full description of the extreme points of the corresponding unit balls and a parametrization and a plot of their unit spheres.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Convexity; Extreme points; Polynomial norms; Trinomials |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 17087 |

References: | R.M. Aron, M. Klimek, Supremum norms for quadratic polynomials, Arch. Math. (Basel) 76 (2001) 73–80. Y.S. Choi, S.G. Kim, The unit ball of P(2l2 2 ), Arch. Math. (Basel) 76 (1998) 472–480. Y.S. Choi, S.G. Kim, Smooth points of the unit ball of the space P(2l1), Results Math. 36 (1999) 26–33. Y.S. Choi, S.G. Kim, Exposed points of the unit balls of the spaces P(2l2p) (p = 1, 2,∞), Indian J. Pure Appl. Math. 35 (2004) 37–41. B.C. Grecu, Geometry of homogeneous polynomials on two-dimensional real Hilbert spaces, J. Math. Anal. Appl. 293 (2) (2004) 578–588. B.C. Grecu, Extreme 2-homogeneous polynomials on Hilbert spaces, Quaest. Math. 25 (4) (2002) 421–435. B.C. Grecu, Geometry of 2-homogeneous polynomials on lp spaces, 1<p<∞, J. Math. Anal. Appl. 273 (2) (2002) 262–282. B.C. Grecu, Smooth 2-homogeneous polynomials on Hilbert spaces, Arch. Math. (Basel) 76 (6) (2001) 445–454. B.C. Grecu, Geometry of three-homogeneous polynomials on real Hilbert spaces, J. Math. Anal. Appl. 246 (1) (2000) 217–229. B.C. Grecu, G.A. Muñoz-Fernández, J.B. Seoane-Sepúlveda, The unit ball of the complex P(3H), preprint. G. Klimek, M. Klimek, Discovering Curves and Surfaces with Maple, New York, 1997. A.G. Konheim, T.J. Rivlin, Extreme points of the unit ball in a space of real polynomials, Amer. Math. Monthly 73 (1966) 505–507. G.A. Muñoz-Fernández, Y. Sarantopoulos, J.B. Seoane-Sepúlveda, An application of the Krein–Milman Theorem to Bernstein and Markov inequalities, preprint. S. Neuwirth, The maximum modulus of a trigonometric trinomial, arXiv:math/FA0703236v1. S. Révész, Minimization of maxima of nonnegative and positive definite cosine polynomials with prescribed first coefficients, Acta Sci. Math. (Szeged) 60 (1995) 589–608. |

Deposited On: | 13 Nov 2012 09:50 |

Last Modified: | 07 Feb 2014 09:41 |

Repository Staff Only: item control page