Summability of Fourier orthogonal expansions and a discretized Fourier orthogonal expansion involving radon projections for functions on the cylinder
Loading...
Date
2009-06
Authors
Wade, Jeremy, 1981-
Journal Title
Journal ISSN
Volume Title
Publisher
University of Oregon
Abstract
We investigate Cesàro summability of the Fourier orthogonal expansion of functions on B d × I m , where B d is the closed unit ball in [Special characters omitted] and I m is the m -fold Cartesian product of the interval [-1, 1], in terms of orthogonal polynomials with respect to the weight functions (1 - z ) α (1 + z ) β (1 - |x| 2 ) λ-1/2 , with z ∈ I m and x ∈ B d . In addition, we study a discretized Fourier orthogonal expansion on the cylinder B 2 × [-1, 1], which uses a finite number of Radon projections. The Lebesgue constant of this operator is obtained, and the proof utilizes generating functions for associated orthogonal series.
Description
vii, 99 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.
Keywords
Fourier orthogonal expansions, Radon projections, Cylindrical functions, Cartesian products, Mathematics