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On Hill's operator with a matrix potential

✍ Scribed by O. A. Veliev

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
144 KB
Volume
281
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

In this article we obtain asymptotic formulas for eigenvalues and eigenfunctions of the self‐adjoint operator generated by a system of Sturm–Liouville equations with summable coefficients and quasiperiodic boundary conditions. Then using these asymptotic formulas, we find conditions on the potential for which the number of gaps in the spectrum of the Hill's operator with matrix potential is finite. (Β© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

πŸ“œ SIMILAR VOLUMES

The Spectral Expansion for a Nonself-adj
The Spectral Expansion for a Nonself-adjoint Hill Operator with a Locally Integrable Potential
✍ O.A. Veliev; M.Toppamuk Duman πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 125 KB

We construct the spectral expansion for the one-dimensional SchrΓΆdinger operator , where q x is a 1-periodic, Lebesgue integrable on [0,1], and complex-valued potential. We obtain the asymptotic formulas for the eigenfunctions and eigenvalues of the operator L t , for t = 0, Ο€, generated by this op