# On the basis property of the root functions of differential operators with matrix coefficients

Open Mathematics (2011)

- Volume: 9, Issue: 3, page 657-672
- ISSN: 2391-5455

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topOktay Veliev. "On the basis property of the root functions of differential operators with matrix coefficients." Open Mathematics 9.3 (2011): 657-672. <http://eudml.org/doc/269755>.

@article{OktayVeliev2011,

abstract = {We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and periodic or antiperiodic boundary conditions. Then using these asymptotic formulas, we find necessary and sufficient conditions on the coefficients for which the system of eigenfunctions and associated functions of the operator under consideration forms a Riesz basis.},

author = {Oktay Veliev},

journal = {Open Mathematics},

keywords = {Differential operators; Eigenfunction expansion; differential operators; eigenfunction expansion; Sturm-Liouville operator; root functions; Riesz basis},

language = {eng},

number = {3},

pages = {657-672},

title = {On the basis property of the root functions of differential operators with matrix coefficients},

url = {http://eudml.org/doc/269755},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Oktay Veliev

TI - On the basis property of the root functions of differential operators with matrix coefficients

JO - Open Mathematics

PY - 2011

VL - 9

IS - 3

SP - 657

EP - 672

AB - We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and periodic or antiperiodic boundary conditions. Then using these asymptotic formulas, we find necessary and sufficient conditions on the coefficients for which the system of eigenfunctions and associated functions of the operator under consideration forms a Riesz basis.

LA - eng

KW - Differential operators; Eigenfunction expansion; differential operators; eigenfunction expansion; Sturm-Liouville operator; root functions; Riesz basis

UR - http://eudml.org/doc/269755

ER -

## References

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- [16] Veliev O.A., Uniform convergence of the spectral expansion for a differential operator with periodic matrix coefficients, Bound. Value Probl., 2008, ID 628973 Zbl1158.34051
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- [18] Veliev O.A., Shkalikov A.A., On the Riesz basis property of the eigen- and associated functions of periodic and antiperiodic Sturm-Liouville problems, Math. Notes, 2009, 85(5–6), 647–660 Zbl1190.34111

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