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- Title
Spectrum and pseudospectrum of non-self-adjoint Schrödinger operators with periodic coefficients.
- Authors
Gal’tsev, S.; Shafarevich, A.
- Abstract
We consider the pseudospectrum of the non-self-adjoint operator , where V( x) is a periodic entire analytic function, real on the real axis, with a real period T. In this operator, h is treated as a small parameter. We show that the pseudospectrum of this operator is the closure of its numerical image, i.e., a half-strip in ℂ. In this case, the pseudoeigenfunctions, i.e., the functions ϕ( h, x) satisfying the condition , can be constructed explicitly. Thus, it turns out that the pseudospectrum of the operator under study is much wider than its spectrum.
- Subjects
SPECTRUM analysis; NONSELFADJOINT operators; SCHRODINGER operator; PERIODIC functions; ANALYTIC functions; EIGENFUNCTIONS; DIFFERENTIAL operators; RIEMANN surfaces
- Publication
Mathematical Notes, 2006, Vol 80, Issue 3/4, p345
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1007/s11006-006-0146-z