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On the nonself-adjoint ordinary differential operators with periodic boundary conditions
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In this paper, asymptotic formulas for eigenvalues and eigenfunctions of the nonself-adjoint ordinary differential operator with periodic and antiperiodic boundary conditions, when coefficients are arbitrary summable complex-valued functions, were obtained.Abstract:
In this article we obtain asymptotic formulas for eigenvalues and eigenfunctions of the nonself-adjoint ordinary differential operator with periodic and antiperiodic boundary conditions, when coefficients are arbitrary summable complex-valued functions. Then using these asymptotic formulas, we obtain necessary and sufficient conditions on the coefficient for which the root functions of these operators form a Riesz basis.read more
Citations
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Criteria for existence of Riesz bases consisting of root functions of Hill and 1D Dirac operators
Plamen Djakov,Boris Mityagin +1 more
TL;DR: In this paper, a series of necessary and sufficient conditions for SRF to contain a Riesz basis in L p -spaces and other rearrangement invariant function spaces are proven.
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Criteria for existence of Riesz bases consisting of root functions of Hill and 1D Dirac operators
Plamen Djakov,Boris Mityagin +1 more
TL;DR: In this article, the system of root functions (SRF) of 1D Dirac operator was studied and necessary and sufficient conditions for SRF to contain a Riesz basis were proven.
Journal ArticleDOI
A Schauder and Riesz basis criterion for non-self-adjoint Schrödinger operators with periodic and antiperiodic boundary conditions
Fritz Gesztesy,Vadim Tkachenko +1 more
TL;DR: In this paper, necessary and sufficient conditions in terms of spectral data for (non-self-adjoint) Schrodinger operators −d2/dx2+V in L2([0,π];dx) with periodic and antiperiodic boundary conditions were derived.
Journal ArticleDOI
Riesz bases consisting of root functions of 1D Dirac operators
Plamen Djakov,Boris Mityagin +1 more
TL;DR: In this paper, the authors give necessary and sufficient conditions on potentials v which guarantee that the system of periodic (or antiperiodic) root functions of LPer±(v) contains Riesz bases.
Journal ArticleDOI
Asymptotic analysis of non-self-adjoint Hill operators
TL;DR: In this paper, the authors obtained uniform asymptotic formulas for the eigenvalues and eigenfunctions of the Sturm-Liouville operators with a potential q ∈ L fixme 1[0, 1] and t-periodic boundary conditions, t ∈ (−π, π).
References
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Boundary problems for ordinary differential equations with parameter in the boundary conditions
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On the basis problem of the eigenfunctions of an ordinary differential operator
Journal ArticleDOI
On the Riesz basis property of the root functions in certain regular boundary value problems
N. B. Kerimov,Kh. R. Mamedov +1 more
TL;DR: In this paper, the differential operatorly=y″+q(x)y with periodic (antiperiodic) boundary conditions that are not strongly regular is studied, and it is shown that the system of root functions of this operator forms a Riesz basis in the spaceL 2(0, 1).
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