Wade, Jeremy, 1981-(University of Oregon, June , 2009)

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Wade, Jeremy, 1981-
2010-03-10T00:12:17Z
2010-03-10T00:12:17Z
2009-06
http://hdl.handle.net/1794/10245
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
en_US
University of Oregon
University of Oregon theses, Dept. of Mathematics, Ph. D., 2009;
Fourier orthogonal expansions
Radon projections
Cylindrical functions
Cartesian products
Mathematics
Summability of Fourier orthogonal expansions and a discretized Fourier orthogonal expansion involving radon projections for functions on the cylinder
Thesis