Complutense University Library

Unconditional constants and polynomial inequalities


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

[img] PDF
Restringido a Repository staff only hasta 2020.


Official URL:


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.

Item Type:Article
Uncontrolled Keywords:Unconditional constant; Polynomial inequalities; Trinomials; Homogeneous polynomials; Extreme points
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16967

Harold P. Boas, Majorant series, J. Korean Math. Soc. 37 (2) (2000) 321–337. Several complex variables (Seoul, 1998).

Yun Sung Choi, Sung Guen Kim, The unit ball of P.2l2 2 /, Arch. Math. (Basel) 71 (6) (1998) 472–480.

Yun Sung Choi, Sung Guen Kim, Haseo Ki, Extreme polynomials and multilinear forms on l1, J. Math. Anal. Appl. 228 (2) (1998) 467–482.

Andreas Defant, Juan Carlos D´ıaz, Domingo Garc´ıa, Manuel Maestre, Unconditional basis and Gordon–Lewis constants for spaces of polynomials, J. Funct. Anal. 181 (1) (2001) 119–145.

Andreas Defant, Leonhard Frerick, A logarithmic lower bound for multi-dimensional Bohr radii, Israel J. Math. 152 (2006) 17–28.

Andreas Defant, Domingo García, Manuel Maestre, Bohr’s power series theorem and local Banach space theory, J. Reine Angew. Math. 557 (2003) 173–197.

Andreas Defant, Domingo García, Manuel Maestre, Estimates for the first and second Bohr radii of Reinhardt domains, J. Approx. Theory 128 (1) (2004) 53–68.

Andreas Defant, Christopher Prengel, Harald Bohr meets Stefan Banach, in: Methods in Banach Space Theory, in: London Math. Soc. Lecture Note Ser., vol. 337, Cambridge Univ. Press, Cambridge, 2006, pp. 317–339.

Bao Qi Feng, Andrew Tonge, Equivalence constants for certain matrix norms. II, Linear Algebra Appl. 420 (2–3) (2007) 388–399.

Bogdan C. Grecu, Geometry of 2-homogeneous polynomials on l p spaces, 1 < p < 1, J. Math. Anal. Appl. 273 (2) (2002) 262–282.

Ren Cang Li, Norms of certain matrices with applications to variations of the spectra of matrices and matrix pencils, Linear Algebra Appl. 182 (1993) 199–234.

Gustavo A. Muñoz-Fernández, Szilard Revesz, Juan B. Seoane-Sepúlveda, Geometry of homogeneous polynomials on non-symmetric convex bodies, Math. Scand (in press).

Gustavo A. Muñoz-Fernández, Juan B. Seoane-Sepúlveda, Geometry of Banach spaces of trinomials, J. Math. Anal. Appl. 340 (2) (2008) 1069–1087.

Stefan Neuwirth, The sidon constant of sets of three elements. arXiv:math.CA/0102145v1.

I. Sarantopoulos, Estimates for polynomial norms on L p. / spaces, Math. Proc. Cambridge Philos. Soc. 99 (2) (1986) 263–271.

Dursun Tas¸ci, On a conjecture by Goldberg and Newman, Linear Algebra Appl. 215 (1995) 275–277.

Deposited On:05 Nov 2012 11:28
Last Modified:14 Mar 2016 17:27

Repository Staff Only: item control page