Pappas, A., Papadopoulos, P., Athanasopoulou, L.. (1394). Polarization constant $\mathcal{K}(n,X)=1$ for entire functions of exponential type. هنرهای کاربردی, 6(2), 35-45. doi: 10.22075/ijnaa.2015.252
A. Pappas; P. Papadopoulos; L. Athanasopoulou. "Polarization constant $\mathcal{K}(n,X)=1$ for entire functions of exponential type". هنرهای کاربردی, 6, 2, 1394, 35-45. doi: 10.22075/ijnaa.2015.252
Pappas, A., Papadopoulos, P., Athanasopoulou, L.. (1394). 'Polarization constant $\mathcal{K}(n,X)=1$ for entire functions of exponential type', هنرهای کاربردی, 6(2), pp. 35-45. doi: 10.22075/ijnaa.2015.252
Pappas, A., Papadopoulos, P., Athanasopoulou, L.. Polarization constant $\mathcal{K}(n,X)=1$ for entire functions of exponential type. هنرهای کاربردی, 1394; 6(2): 35-45. doi: 10.22075/ijnaa.2015.252

Polarization constant $\mathcal{K}(n,X)=1$ for entire functions of exponential type

International Journal of Nonlinear Analysis and Applications
مقاله 4، دوره 6، شماره 2، 2015، صفحه 35-45    اصل مقاله (406.11 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2015.252
نویسندگان
A. Pappas* 1؛ P. Papadopoulos2؛ L. Athanasopoulou3
1Civil Engineering Department, School of Technological Applications, Piraeus University of Applied Sciences (Technological Education Institute of Piraeus), GR 11244, Egaleo, Athens, Greece
2adepartment of electronics engineering, school of technological applications, technological educational institution (tei) of piraeus, gr 11244, egaleo, athens, Greece.
3Department of Electronics Engineering, School of Technological Applications, Piraeus University of Applied Sciences (Technological Education Institute of Piraeus), GR 11244, Egaleo, Athens, Greece
چکیده
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.
کلیدواژه‌ها
Polarization constants؛ polynomials on Banach spaces؛ polarization formulas
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