Some Special Tauberian Theorems for Fourier Type Integrals and Eigenfunction Expansions of Sturm-Liouville Equations on the Whole Line

1995 ◽  
Vol 176 (1) ◽  
pp. 179-198 ◽  
Author(s):  
B. M. Levitan
Keyword(s):  
Tauberian Theorems ◽  
Eigenfunction Expansions ◽  
Sturm Liouville ◽  
Fourier Type

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.

B*-algebra eigenfunction expansions

1980 ◽  
Vol 86 (3-4) ◽  
pp. 307-314
Author(s):  
Manuel Lopez
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Regular Boundary ◽  
Eigenfunction Expansions ◽  
Expansion Theorem ◽  
Sturm Liouville

SynopsisIn this paper the Sturm-Liouville regular boundary value problem and expansion theorem is extended to functions with values in some B*-algebras.

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