Summability of Fourier orthogonal expansions and a discretized Fourier orthogonal expansion involving radon projections for functions on the cylinder

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Title: Summability of Fourier orthogonal expansions and a discretized Fourier orthogonal expansion involving radon projections for functions on the cylinder
Author: Wade, Jeremy, 1981-
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.
URI: http://hdl.handle.net/1794/10245
Date: 2009-06


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