Vol. 7, No. 1, 2014

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Orthonormal systems in linear spans

Allison Lewko and Mark Lewko

Vol. 7 (2014), No. 1, 97–115
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 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.

Keywords
orthogonal systems, square variation, maximal operator, Fourier analysis
Mathematical Subject Classification 2010
Primary: 42A61, 42B05, 42C05
Milestones
Received: 10 May 2012
Revised: 26 February 2013
Accepted: 3 April 2013
Published: 7 May 2014
Authors
Allison Lewko
Department of Computer Science
Columbia University
1214 Amsterdam Avenue, MC 0401
New York, NY 10027
United States
Mark Lewko
Department of Mathematics
University of California, Los Angeles
520 Portola Plaza
Math Sciences Building 6363
Los Angeles, CA 90095
United States