scholarly journals Essential spectral singularities and the spectral expansion for the Hill operator

2017 ◽  
Vol 16 (6) ◽  
pp. 2227-2251 ◽  
Author(s):  
O. A. Veliev ◽  
Keyword(s):  
Spectral Expansion ◽  
Hill Operator ◽  
Spectral Singularities ◽  
The Hill

scholarly journals Asymptotic analysis of non-self-adjoint Hill operators

2013 ◽  
Vol 11 (12) ◽  
Author(s):  
Oktay Veliev
Keyword(s):  
Sufficient Conditions ◽  
Periodic Boundary Conditions ◽  
Asymptotic Formulas ◽  
Spectral Operator ◽  
Hill Operator ◽  
Eigenvalues And Eigenfunctions ◽  
Spectral Singularities ◽  
Sturm Liouville ◽  
The Hill ◽  
Liouville Operators

AbstractWe obtain uniform asymptotic formulas for the eigenvalues and eigenfunctions of the Sturm-Liouville operators L t (q) with a potential q ∈ L 1[0,1] and t-periodic boundary conditions, t ∈ (−π, π]. Using these formulas, we find sufficient conditions on the potential q such that the number of spectral singularities in the spectrum of the Hill operator L(q) in L 2(−∞,∞) is finite. Then we prove that the operator L(q) has no spectral singularities at infinity and it is an asymptotically spectral operator provided that the potential q satisfies sufficient conditions.

Spectral properties of the Hill operator

2016 ◽  
Vol 99 (3-4) ◽  
pp. 598-602 ◽  
Author(s):  
A. G. Baskakov ◽  
D. M. Polyakov
Keyword(s):  
Spectral Properties ◽  
Hill Operator ◽  
The Hill

scholarly journals Estimates for the Hill operator, II

2006 ◽  
Vol 223 (2) ◽  
pp. 229-260 ◽  
Author(s):  
Evgeny Korotyaev
Keyword(s):  
Hill Operator ◽  
The Hill

scholarly journals The inverse problem for the Hill operator, a direct approach

1997 ◽  
Vol 129 (3) ◽  
pp. 567-593 ◽  
Author(s):  
Pavel Kargaev ◽  
Evgeni Korotyaev
Keyword(s):  
Inverse Problem ◽  
Direct Approach ◽  
Hill Operator ◽  
The Hill
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