On the riesz basisness of the root functions of the nonself-adjoint sturm-liouville operator
By Neşe Dernek, O. Veliev. 2005
50 citations recorded by the source corpus.
In this article we obtain the asymptotic formulas for eigenfunctions and eigenvalues of the nonself-adjoint Sturm-Liouville operators with periodic and antiperiodic boundary conditions, when the potential is an arbitrary summable complex-valued function. Then using these asymptotic formulas, we find the conditions on Fourier coefficients of the potential for which the eigenfunctions and associated functions of these operators form a Riesz basis inL2(0, 1).
Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/9b6decf6a0991ffa0896d765fb649ffab2d0d474
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In Atomic and Molecular Physics, and Optics
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- A criterion for Hill operators to be spectral operators of scalar type (2006, background): “made essential progress in studying the same property for systems of eigenfunctions of two-point boundary problems for higher-order differential operators, and Dernek and Veliev [ 9 ] and Makin [37] found sufficient conditions for the root system of a Schr¨ odinger operator on the interval [0,1] ass”
- A Schauder and Riesz Basis Criterion for Non-Self-Adjoint Schr\ (2011, methodology): “Having in mind the periodic/antiperiodic boundary problems for Schrödinger operators only, we note that most results in this context were obtained under assumptions which restrict the smoothness properties of potentials, see, for instance, [8], [38], [40], [42], [48], [49], [53], [54], and [57].”