## Abstract

In this paper we prove the main step in establishing a limiting absorption principle for von Neumann-Wigner type Schrödinger Hamiltonians of the form -Δ+csinb|x|/|x|+V(x), where V(x) is a short range potential. The first fundamental step is to obtain a limiting absorption principal for the "free" operator -Δ+csinb.|x|/|x|. The free operator is unitarily equivalent to a direct sum of ordinary differential operators. We obtain uniform estimates for the resolvents of these ordinary differential operators. by obtaining uniform estimates for the Weyl-Green kernels of these resolvents. In turn, these latter estimates require uniform estimates on the Wronskians of certain generalized eigen-solutions of these differential operators.

Original language | English (US) |
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Pages (from-to) | 13-68 |

Number of pages | 56 |

Journal | Integral Equations and Operator Theory |

Volume | 14 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1991 |