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The computation of spectral density functions for singular Sturm-Liouville problems involving simple continuous spectra

✍ Scribed by Fulton, C. T.; Pruess, S.

Book ID
115514485
Publisher
Association for Computing Machinery
Year
1998
Tongue
English
Weight
192 KB
Volume
24
Category
Article
ISSN
0098-3500

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✦ Synopsis

The software package SLEDGE has as one of its options the estimation of spectral density functions
p(t)
for a wide class of singular Strurm-Liouville problems. In this article the underlaying theory and implementation issues are discussed. Several examples exhibiting quite varied asymptotic behavior in
p
are presented.

πŸ“œ SIMILAR VOLUMES

New characterizations of spectral densit
New characterizations of spectral density functions for singular Sturm–Liouville problems
✍ Charles Fulton; David Pearson; Steven Pruess πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 244 KB

A generalization is given for a characterization of the spectral density function of Weyl and Titchmarsh for a singular Sturm-Liouville problem having absolutely continuous spectrum in [0, ∞). A recurrent formulation is derived that generates a family of approximations based on this scheme. Proofs o

Efficient calculation of spectral densit
Efficient calculation of spectral density functions for specific classes of singular Sturm–Liouville problems
✍ Charles Fulton; David Pearson; Steven Pruess πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 285 KB

New families of approximations to Sturm-Liouville spectral density functions are derived for cases where the potential function has one of several specific forms. This particular form dictates the type of expansion functions used in the approximation. Error bounds for the residuals are established f