title   
  

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

Djakov, 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

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Official URL: http://dx.doi.org/10.1016/j.jfa.2013.05.003

Abstract

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.

Item Type:Article
Uncontrolled Keywords:Hill operators; Periodic and antiperiodic boundary conditions; Two exponential term potentials
Subjects:Q Science > QA Mathematics > QA299.6-433 Analysis
ID Code:21978
Deposited By:Plamen Borissov Djakov
Deposited On:07 Nov 2013 16:04
Last Modified:07 Nov 2013 16:04

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