Eigenfunction Expansions for a Sturm-Liouville Operator for the Case of an Infinite Interval

1975 ◽  
pp. 101-166
Keyword(s):  
Liouville Operator ◽  
Infinite Interval ◽  
Eigenfunction Expansions ◽  
Sturm Liouville

On the divergence in rth mean of a class of eigenfunction expansions

1979 ◽  
Vol 84 (3-4) ◽  
pp. 347-363
Author(s):  
C. G. C. Pitts
Keyword(s):  
Eigenfunction Expansion ◽  
Liouville Problem ◽  
Infinite Interval ◽  
Series Expansions ◽  
Eigenfunction Expansions ◽  
Series Form ◽  
Unbounded Sequence ◽  
Measurable Functions ◽  
Sturm Liouville ◽  
Hermite Series

SynopsisWe consider the expansion of a function in Lr (the class of measurable functions whose rth powers are Lebesgue integrable over some interval) in terms of the eigenfunctions arising from a singular Sturm-Liouville problem defined over an infinite or semi-infinite interval. We show that if l ≦ r ≦ inline1 or if r ≧ 4 there exists f in Lr whose eigenfunction expansion is divergent in the rth mean sense, and that the terms of the series form an unbounded sequence in Lr The result extends some work of Askey and Wainger concerning the Hermite series expansions of functions in Lr(–∞, ∞).

Ambarzumyan-type theorem for the impulsive Sturm–Liouville operator

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ran Zhang ◽  
Chuan-Fu Yang
Keyword(s):  
Liouville Operator ◽  
Type Theorem ◽  
Sturm Liouville ◽  
Neumann Laplacian ◽  
Neumann Eigenvalues

AbstractWe prove that if the Neumann eigenvalues of the impulsive Sturm–Liouville operator {-D^{2}+q} in {L^{2}(0,\pi)} coincide with those of the Neumann Laplacian, then {q=0}.

scholarly journals Recovering the M-channel Sturm-Liouville operator from M+1 spectra

2004 ◽  
Vol 45 (11) ◽  
pp. 4255-4260 ◽  
Author(s):  
V. M. Chabanov
Keyword(s):  
Liouville Operator ◽  
Sturm Liouville

Spectral analysis for the Sturm–Liouville operator on sun-type graphs

2011 ◽  
Vol 27 (9) ◽  
pp. 095003 ◽  
Author(s):  
Gerhard Freiling ◽  
Mikhail Ignatyev
Keyword(s):  
Spectral Analysis ◽  
Liouville Operator ◽  
Sturm Liouville
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