@article {
author = {Pappas, A. and Papadopoulos, P. and Athanasopoulou, L.},
title = {Polarization constant $\mathcal{K}(n,X)=1$ for entire functions of exponential type},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {6},
number = {2},
pages = {35-45},
year = {2015},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2015.252},
abstract = {In this paper we will prove that if $L$ is a continuous symmetric n-linear form on a Hilbert space and $\widehat{L}$ is the associated continuous n-homogeneous polynomial, then $||L||=||\widehat{L}||$. For the proof we are using a classical generalized inequality due to S. Bernstein for entire functions of exponential type. Furthermore we study the case that if X is a Banach space then we have that$$|L|=|\widehat{L}|, \forall L \in{\mathcal{L}}^{s}(^{n}X).$$If the previous relation holds for every $L \in {\mathcal{L}}^{s}\left(^{n}X\right)$, then spaces ${\mathcal{P}}\left(^{n}X\right)$ and $L \in {\mathcal{L}}^{s}(^{n}X)$ are isometric. We can also study the same problem using Fr$\acute{e}$chet derivative.},
keywords = {Polarization constants,polynomials on Banach spaces,polarization formulas},
url = {https://ijnaa.semnan.ac.ir/article_252.html},
eprint = {https://ijnaa.semnan.ac.ir/article_252_67988509b46f50477e7aba6e7d056fd0.pdf}
}