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

100%

Veliev O.

Open Mathematics

2011

tom 9

nr 3

657-672

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.

Inverse problems on star-type graphs: differential operators of different orders on different edges

80%

Yurko V.

Open Mathematics

2014

tom 12

nr 3

483-499

We study inverse spectral problems for ordinary differential equations on compact star-type graphs when differential equations have different orders on different edges. As the main spectral characteristics we introduce and study the so-called Weyl-type matrices which are generalizations of the Weyl function (m-function) for the classical Sturm-Liouville operator. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness.

Ograniczanie wyników

2 Open Mathematics

1 Veliev O.

1 Yurko V.

1 2014

1 2011

Wyniki wyszukiwania

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

Inverse problems on star-type graphs: differential operators of different orders on different edges