Orthonormal Systems in Linear Spans
ANALYSIS & PDE(2014)
摘要
We show that any N-dimensional linear subspace of L-2 (T) admits an orthonormal system such that the L-2 norm of the square variation operator V-2 is as small as possible. When applied to the span of the trigonometric system, we obtain an orthonormal system of trigonometric polynomials with a V-2 operator that is considerably smaller than the associated operator for the trigonometric system itself.
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关键词
orthogonal systems,square variation,maximal operator,Fourier analysis
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