Abstract
Given a finite orthonormal sequence (Error rendering LaTeX formula) in some and vectors in some Banach space X we are interested in the norm of the sums (Error rendering LaTeX formula) in .A constuction in [1] suggests that the system may be replaced by the set (Error rendering LaTeX formula) of coordinate functions (Error rendering LaTeX formula) on viewed as un orthonormal system with respect to a suitable measure λ on .We show by a convolutional argument that after symmetrization the measure λ is uniquely determined.We also discuss related questions.
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