scholarly journals Sturm–Liouville Problems with Transfer Condition Herglotz Dependent on the Eigenparameter: Hilbert Space Formulation

2018 ◽  
Vol 90 (3) ◽  
Author(s):  
Casey Bartels ◽  
Sonja Currie ◽  
Marlena Nowaczyk ◽  
Bruce Alastair Watson
Keyword(s):  
Hilbert Space ◽  
Transfer Condition ◽  
Space Formulation ◽  
Sturm Liouville

Full- and partial-range eigenfunction expansions for Sturm-Liouville problems with indefinite weights

1984 ◽  
Vol 98 (1-2) ◽  
pp. 69-88 ◽  
Author(s):  
Hans G. Kaper ◽  
Man Kam Kwong ◽  
C. G. Lekkerkerker ◽  
A. Zettl
Keyword(s):  
Hilbert Space ◽  
Differential Expression ◽  
Positive Operator ◽  
Eigenvalue Problems ◽  
Full Range ◽  
Second Order ◽  
Eigenfunction Expansions ◽  
Multiplicative Operator ◽  
Indefinite Weights ◽  
Sturm Liouville

SynopsisThis article is concerned with eigenvalue problems of the form Au = λTu in a Hilbert space H, where Ais a selfadjoint positive operator generated by a second-order Sturm-Liouville differential expression and T a selfadjoint indefinite multiplicative operator which is one-to-one. Emphasis is on the full-range and partial-range expansionproperties of the eigenfunctions.

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