Wade, Jeremy, 1981-2010-03-102010-03-102009-06https://hdl.handle.net/1794/10245vii, 99 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.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.en-USFourier orthogonal expansionsRadon projectionsCylindrical functionsCartesian productsMathematicsThesis