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. / 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. / Committee in charge: Yuan Xu, Chairperson, Mathematics;
Huaxin Lin, Member, Mathematics
Jonathan Brundan, Member, Mathematics;
Marcin Bownik, Member, Mathematics;
Jun Li, Outside Member, Computer & Information Science
| Identifer | oai:union.ndltd.org:uoregon.edu/oai:scholarsbank.uoregon.edu:1794/10245 |
| Date | 06 1900 |
| Creators | Wade, Jeremy, 1981- |
| Publisher | University of Oregon |
| Source Sets | University of Oregon |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
| Relation | University of Oregon theses, Dept. of Mathematics, Ph. D., 2009; |
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