Virginia Polytechnic Institute
Notes on generalized Fourier series with application to gravitational field determination
Abstract
dc:description.abstractLet{(}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.
Degree
thesis:*- Name thesis:degree_name
- M.S.
- Level thesis:degree_level
- masters
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Polytechnic Institute
- Year dc:date.issued
- 1967
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Blackshear, Walter Thomas
Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
- Language dc:language.iso
- en
Identifiers
dc:identifier.*- Handle dc:identifier.uri
- http://hdl.handle.net/10919/106206
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/106206