Spectral Properties of a Singular Differential Operator on an Interval with Transmission Conditions
We study the first boundary value problem for a second-order differential operator with a singular coefficient on an interval with transmission conditions at an interior point. Asymptotic formulas are obtained for the eigenfunctions and eigenvalues of both the original and the adjoint operator. The...
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| Veröffentlicht in: | Differential equations 2023-05, Vol.59 (5), p.591-596 |
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| container_title | Differential equations |
| container_volume | 59 |
| creator | Lomov, I. S. |
| description | We study the first boundary value problem for a second-order differential operator with a singular coefficient on an interval with transmission conditions at an interior point. Asymptotic formulas are obtained for the eigenfunctions and eigenvalues of both the original and the adjoint operator. The completeness and unconditional basis property of the eigenfunction systems of these operators in the space of square integrable functions on the interval are established. Il’in’s method and Il’in’s conditions are applied to establish the Bessel inequality. |
| doi_str_mv | 10.1134/S0012266123050026 |
| format | Article |
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Il’in’s method and Il’in’s conditions are applied to establish the Bessel inequality.</description><subject>Boundary value problems</subject><subject>Difference and Functional Equations</subject><subject>Differential equations</subject><subject>Eigenvalues</subject><subject>Eigenvectors</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operators (mathematics)</subject><subject>Ordinary Differential Equations</subject><subject>Partial Differential Equations</subject><issn>0012-2661</issn><issn>1608-3083</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LAzEQhoMoWKs_wFvA8-rMppvNHqV-QkGhel7iZlIjbVKTVPHfm1LBg8gcMsz7PjOZYewU4RxRTC7mAFjXUmItoAGo5R4boQRVCVBin422crXVD9lRSm8A0LXYjNgwX9OQo17yxxjWFLOjxIPlms-dX2yWOvIrZy1F8tkV10Px6BwiD55rz-99pvhR6p8uv_KnqH1auZRcUafBG5dLlo7ZgdXLRCc_75g931w_Te-q2cPt_fRyVg0C2lw12rSotFSWTNtKIqNfWpwIrTSiAUsKBZhG2VYYWdbsqO66xkg02EykQDFmZ7u-6xjeN5Ry_xY20ZeRfa0mQjUdlHZjdr5zLfSSeudtKOsPJQyt3BA8WVfql23TIYLq6gLgDhhiSCmS7dfRrXT86hH67fH7P8cvTL1jUvH6BcXfr_wPfQPMGIWk</recordid><startdate>20230501</startdate><enddate>20230501</enddate><creator>Lomov, I. 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| fulltext | fulltext |
| identifier | ISSN: 0012-2661 |
| ispartof | Differential equations, 2023-05, Vol.59 (5), p.591-596 |
| issn | 0012-2661 1608-3083 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Boundary value problems Difference and Functional Equations Differential equations Eigenvalues Eigenvectors Mathematics Mathematics and Statistics Operators (mathematics) Ordinary Differential Equations Partial Differential Equations |
| title | Spectral Properties of a Singular Differential Operator on an Interval with Transmission Conditions |
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