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Spectrum of singular Sturm-Liouville operators with singular interior point

  1. Nov 12, 2012 #1
    Hi,

    I have a singular Sturm-Liouville problem with LCNO end-points, but also one limit circle point in the interior of the interval. Suppose I take boundary conditions that get me a self-adjoint extension of the differential operator, does anyone know if that gives me a discrete spectrum?

    The SL operator is:
    L(d,dx) f(x) = (P(x) f'(x))' + 2x^2 f(x), x in (-2,1)

    P(x) = (x^2-1)(x^2-4)

    So the boundaries +1 and -2 are limit circle end-points, but there is one more singularity at -1.

    Thanks
     
  2. jcsd
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