### Abstract

He present work deals with estimations of the n-th linear polarization constant c(H) _{n} of an n-dimensional real Hilbert space H. We provide some new lower bounds on the value of sup _{∥y∥=1} |〈x _{1},y〉 ... 〈x _{n},y〉|, where x _{1}, ... ,x _{n} are unit vectors in H. In particular, the results improve an earlier estimate of Marcus. However, the intriguing conjecture c(H) _{n}= n ^{n/2} remains open.

Original language | English |
---|---|

Pages (from-to) | 129-136 |

Number of pages | 8 |

Journal | Acta Mathematica Hungarica |

Volume | 108 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Jul 2005 |

### Fingerprint

### Keywords

- Gram matrices
- Linear polarization constants
- Polynomials over normed spaces

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

^{n}

*Acta Mathematica Hungarica*,

*108*(1-2), 129-136. https://doi.org/10.1007/s10474-005-0214-y

**The linear polarization constant of R ^{n} .** / Matolcsi, M.

Research output: Contribution to journal › Article

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*Acta Mathematica Hungarica*, vol. 108, no. 1-2, pp. 129-136. https://doi.org/10.1007/s10474-005-0214-y

^{n}Acta Mathematica Hungarica. 2005 Jul;108(1-2):129-136. https://doi.org/10.1007/s10474-005-0214-y

}

TY - JOUR

T1 - The linear polarization constant of R n

AU - Matolcsi, M.

PY - 2005/7

Y1 - 2005/7

N2 - He present work deals with estimations of the n-th linear polarization constant c(H) n of an n-dimensional real Hilbert space H. We provide some new lower bounds on the value of sup ∥y∥=1 |〈x 1,y〉 ... 〈x n,y〉|, where x 1, ... ,x n are unit vectors in H. In particular, the results improve an earlier estimate of Marcus. However, the intriguing conjecture c(H) n= n n/2 remains open.

AB - He present work deals with estimations of the n-th linear polarization constant c(H) n of an n-dimensional real Hilbert space H. We provide some new lower bounds on the value of sup ∥y∥=1 |〈x 1,y〉 ... 〈x n,y〉|, where x 1, ... ,x n are unit vectors in H. In particular, the results improve an earlier estimate of Marcus. However, the intriguing conjecture c(H) n= n n/2 remains open.

KW - Gram matrices

KW - Linear polarization constants

KW - Polynomials over normed spaces

UR - http://www.scopus.com/inward/record.url?scp=22044455843&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22044455843&partnerID=8YFLogxK

U2 - 10.1007/s10474-005-0214-y

DO - 10.1007/s10474-005-0214-y

M3 - Article

VL - 108

SP - 129

EP - 136

JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

SN - 0236-5294

IS - 1-2

ER -