Let{(}φ<sub>n</sub>(x)} be an orthonormal system in the set of Lebesgue square integrable functions L². Let f𝜖L². The generalized Fourier series of f with respect to {(}φ<sub>n</sub>(x)} is the series ∑<sub>n=0</sub><sup>∞</sup> (f, φ<sub>n</sub>) φ<sub>n</sub>(x), where (f, φ<sub>n</sub>) is the inner product of the functions f an φ<sub>n</sub>. The e existence of a complete orthonormal system in L² is proven. Conditions for convergence of the generalized Fourier series are presented. A discussion of orthogonal polynomials with special emphasis on the Jacobi polynomial systems is presented. A least squares, differential correction, discrete observation procedure is employed to solve the potential equation with boundary conditions in tenns of three special Jacobi systems. / M.S.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/106206 |
| Date | January 1967 |
| Creators | Blackshear, Walter Thomas |
| Contributors | Mathematics |
| Publisher | Virginia Polytechnic Institute |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis, Text |
| Format | 114 leaves, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 20395399 |
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