scholarly journals Inverse Spectral and Scattering Theory for the Half-Line Left-Definite Sturm–Liouville Problem

2009 ◽  
Vol 40 (5) ◽  
pp. 2105-2131 ◽  
Author(s):  
C. Bennewitz ◽  
B. M. Brown ◽  
R. Weikard
Keyword(s):  
Scattering Theory ◽  
Liouville Problem ◽  
Half Line ◽  
Sturm Liouville ◽  
Inverse Spectral ◽  
Spectral And Scattering Theory

A generalisation of the inverse spectral theorem of Levitan and Gasymov

1979 ◽  
Vol 84 (3-4) ◽  
pp. 185-196 ◽  
Author(s):  
Christine Thurlow
Keyword(s):  
Spectral Function ◽  
Sufficient Conditions ◽  
Liouville Problem ◽  
Necessary And Sufficient Conditions ◽  
Spectral Theorem ◽  
Sturm Liouville ◽  
Inverse Spectral ◽  
Image Position ◽  
Necessary And Sufficient

SynopsisIn the Inverse Spectral Theorem in the form given by Levitan and Gasymov, necessary and sufficient conditions are given for a non-decreasing function, p(ℷ), to be the spectral function of a Sturm–Liouville problem. In these conditions, p(ℷ) is compared with the spectral function for the particular Strum–Liouville problemIf the method of Levitan and Gasymov's proof is slightly adapted, the necessary and sufficient conditions can be stated in a more general form in which p(ℷ) is compared with the spectral function for any problem of the formwherehOis real and qo(x) locally integrable.

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