Cesaro-One Summability and Uniform Convergence of Solutions of a Sturm-Liouville System
- Sandia National Laboratories
Galerkin methods are used in separable Hilbert spaces to construct and compute L{sup 2} [0,{pi}] solutions to large classes of differential equations. In this note a Galerkin method is used to construct series solutions of a nonhomogeneous Sturm-Liouville problem defined on [0,{pi}]. The series constructed are shown to converge to a specified du Bois-Reymond function f in L{sup 2} [0,{pi}]. It is then shown that the series solutions can be made to converge uniformly to the specified du Bois-Reymond function when averaged by the Ces{'a}ro-one summability method. Therefore, in the Ces{'a}ro-one sense, every continuous function f on [0,{pi}] is the uniform limit of solutions of nonhomogeneous Sturm-Liouville problems.
- Research Organization:
- Sandia National Laboratories, Albuquerque, NM, and Livermore, CA
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC04-94AL85000
- OSTI ID:
- 3223
- Report Number(s):
- SAND99-0177J; ON: DE00003223
- Journal Information:
- Real Analysis Exchange, Journal Name: Real Analysis Exchange
- Country of Publication:
- United States
- Language:
- English
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