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2014 Orthonormal systems in linear spans
Allison Lewko, Mark Lewko
Anal. PDE 7(1): 97-115 (2014). DOI: 10.2140/apde.2014.7.97

Abstract

We show that any N-dimensional linear subspace of L2(T) admits an orthonormal system such that the L2 norm of the square variation operator V2 is as small as possible. When applied to the span of the trigonometric system, we obtain an orthonormal system of trigonometric polynomials with a V2 operator that is considerably smaller than the associated operator for the trigonometric system itself.

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Allison Lewko. Mark Lewko. "Orthonormal systems in linear spans." Anal. PDE 7 (1) 97 - 115, 2014. https://doi.org/10.2140/apde.2014.7.97

Information

Received: 10 May 2012; Revised: 26 February 2013; Accepted: 3 April 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1298.42032
MathSciNet: MR3219501
Digital Object Identifier: 10.2140/apde.2014.7.97

Subjects:
Primary: 42A61 , 42B05 , 42C05

Keywords: Fourier analysis , Maximal operator , orthogonal systems , Square variation

Rights: Copyright © 2014 Mathematical Sciences Publishers

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