Divergence of spectral decompositions of Hill operators with two exponential term potentials

作者：Djakov Plamen^*; Mityagin Boris

来源：Journal of Functional Analysis, 2013, 265(4): 660-685.

DOI：10.1016/j.jfa.2013.05.003

• Hill operators
• Periodic and antiperiodic boundary conditions
• Two exponential term potentials

We 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.

• 出版日期2013-8-15