Spectral properties of an even-order differential operator. (English. Russian original) Zbl 1353.47088
Differ. Equ. 52, No. 8, 1098-1103 (2016); translation from Differ. Uravn. 52, No. 8, 1133-1137 (2016).
Summary: We present the spectral properties of an even-order differential operator whose domain is described by periodic and antiperiodic boundary conditions or the Dirichlet conditions. We derive an asymptotic formula for the eigenvalues, estimates for the deviations of spectral projections, and estimates for the equiconvergence rate of spectral decompositions. Our asymptotic formulas for eigenvalues refine well-known ones.
MSC:
| 47E05 | General theory of ordinary differential operators |
| 34L20 | Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators |
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