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Sektion 2
Dienstag, 19.09.2000, 17.30–17.50 Uhr, POT 6

On the Eigenvalue Accumulation of the Radial Dirac Operator with Potential

Harald Schmid, Universität Regensburg, NWF I - Mathematik

For piecewise continuous potentials which „behave like“ power functions at 0 and  oo we investigate whether the discrete eigenvalues of the radial Dirac operator accumulate at +1 or not. The main theorem is an accumulation/nonaccumulation criterion where only the constants of the involved power functions appear. We obtain this result by a method which is based on a Levinson type theorem for asymptotically diagonal systems depending on some parameter, a comparison theorem for the principal solutions of regular singular systems and some accumulation/nonaccumulation criteria for nonlinear singular Sturm-Liouville problems. As a second application of this method, we get a similar criterion on the eigenvalue accumulation at 0 for the radial Schrödinger equation.