Divergence of spectral decompositions of Hill operators with two exponential term potentialsDjakov, Plamen Borissov and Mityagin, Boris Samuel (2013) Divergence of spectral decompositions of Hill operators with two exponential term potentials. Journal of Functional Analysis, 265 (4). pp. 660-685. ISSN 0022-1236 Full text not available from this repository. Official URL: http://dx.doi.org/10.1016/j.jfa.2013.05.003 AbstractWe consider the Hill operator Ly = -y '' + v(x)y, 0 <= x <= pi, subject to periodic or antiperiodic boundary conditions (bc) with potentials of the form v(x) = ae(-2irx) + be(2isx), a, b not equal 0, r, s is an element of N, r not equal s. It is shown that the system of root functions does not contain a basis in L-2([0, pi], C) if bc are periodic or if bc are antiperiodic and r, s are odd or r = 1 and s >= 3.
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