Some aspects of the theory of time and band limited operators associated with Lame's equation
Technical Report
·
OSTI ID:5071483
The thesis has three chapters. In Chapter 1, it introduces the Gegenbauer functions and their fundamental properties. Following Grunbaum, it proves that the partial Gram matrix for Gegenbauer's equation admits a commuting tridiagonal matrix. Chapter 2 discusses the rudiments of the theory of the Weierstrass P-function and associated functions, and investigates in some detail the Sturm-Liouville problem for Lame's equation. Chapter 3 is the central chapter of the thesis. After beginning with some algebraic preliminaries concerning the linear equations which determine the existence of a commuting tridiagonal matrix, it presents the non-existence proof for dimension four, as well as the numerical evidence. This chapter concludes with a discussion of some numerical experiments which suggest a means of conducting the spectral analysis of the partial Gram matrix even when no commuting tridiagonal matrix exists. Finally, the appendix describes the algorithms used to evaluate the functions P, sigma, and zeta.
- Research Organization:
- Lawrence Berkeley Lab., CA (USA)
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 5071483
- Report Number(s):
- LBL-17570; ON: DE84010711
- Country of Publication:
- United States
- Language:
- English
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