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On vector-valued random Fourier series

Authors:

Institution:

1. Equipe d'Analyse-Tour 46, University of Paris VI, 4 Place Jussieu, 75230, Paris Cedex 05
2. Department of Mathematics, The Ohio State University, 43210, Columbus, Ohio

Abstract:

Consider a (complex) Banach spaceX, such thatX nsup

C_O, and vectors(X _i)_i ofX. Consider an independent standard normal sequence(g _i)_i. Then if anX-valued random Fourier series sum

_|k|

_n e ^ikt g _k x _k satisfies

$\mathop {\sup }\limits_n E\mathop {\sup }\limits_{\left\| t \right\| \leqslant 1} \left\\| {\sum\limits_{\left\| k \right\| \leqslant n} {e^{ikt} g_k x_k } } \right\\|< \infty$

Keywords:	Random Fourier series complex Banach space
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