Talk page
Title:
1-Dim Half-line Schrödinger Operators with H^{-1} Potentials
Speaker:
Abstract:
In this talk, I will present some spectral results of Schrödinger operators with locally H^{-1} potentials. In the first part, we will recover some general spectral theoretical results in the current setting, including a Last-Simon-type criteria for the presence and absence of the absolutely continuous spectrum on the open half-line. In the second part, we will focus on potentials which are decaying in a locally H^{-1} sense and present an analogue of short-range decay in the distributional setting. In particular, we will examine a class of Pearson-type distributional potentials and establish a spectral transition between short-range and long-range decay.
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