Orthonormal systems in linear spans

Allison Lewko, Mark Lewko

Type: Article

Publication Date: 2014-05-07

Citations: 5

DOI: https://doi.org/10.2140/apde.2014.7.97

Abstract

We show that any N -dimensional linear subspace of L 2 ‫)ޔ(‬ 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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Analysis & PDE - View - PDF
arXiv (Cornell University) - View - PDF
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+ PDF Chat	An exact asymptotic for the square variation of partial sum processes	2015	Allison Lewko Mark Lewko
+ PDF Chat	Sidonicity and variants of Kaczmarz’s problem	2017	Jean Bourgain Mark Lewko
+ PDF Chat	The square variation of rearranged Fourier series	2015	Allison Lewko Mark Lewko
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+	The Square Variation of Rearranged Fourier Series	2012	Allison Lewko Mark Lewko

Works Cited by This (9)

Action	Title	Year	Authors
+	On kolmogorov's rearrangement problem for orthogonal systems and garsia's conjecture	2006	Jean Bourgain
+	Random Fourier Series with Applications to Harmonic Analysis	1981	Michael B. Marcus
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+	An Exact Asymptotic for the Square Variation of Partial Sum Processes	2011	Allison Lewko Mark Lewko
+ PDF Chat	A variation norm Carleson theorem	2012	Richard Oberlin Andreas Seeger Terence Tao Christoph Thiele James Wright
+	Random factorization of operators between Banach spaces	1981	Yoav Benyamini Y. Gordon
+	The Sizes of Compact Subsets of Hilbert Space and Continuity of Gaussian Processes	2010	R. M. Dudley
+	A variational Barban–Davenport–Halberstam Theorem	2012	Allison Lewko Mark Lewko
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