Basic Sturm -Liouville Theory

• Harold Exton Penwortham. Preston-Reino Unido

Resumo

In the real domain, a basic analogue of a simple form of Sturm Liouville equation of the second order is studied, and it is shown that, with proper boundary conditions, its solutions are orthogonal with respect to basic integration. Basic functions which are analogous to the sine and cosine are briefly discussed and are utilised in an investigation of the conditions that solutions of the equation under consideration should be oscillatory . Final1y, it is shown that an arbitrary function may be expanded in a series of basic eigen-functions. In the limit as q, the base, tends to unity, we recover results which are well-known in ordinary Sturm-Liouville theory.