Orthonormal systems in linear spans
Copyright policy )Orthonormal systems in linear spans
We show that any $N$-dimensional linear subspace of $L^2(\mathbb{T})$ 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.
18 pages
- King’s University United States
- Columbia University, USA United States
- University of California, Los Angeles United States
42B05, square variation, 42C05, Fourier series and coefficients in several variables, Probability (math.PR), Fourier analysis, orthogonal systems, Mathematics - Classical Analysis and ODEs, 42A61, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, maximal operator, Probabilistic methods for one variable harmonic analysis, Mathematics - Probability
42B05, square variation, 42C05, Fourier series and coefficients in several variables, Probability (math.PR), Fourier analysis, orthogonal systems, Mathematics - Classical Analysis and ODEs, 42A61, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, maximal operator, Probabilistic methods for one variable harmonic analysis, Mathematics - Probability
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