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Function spaces associated with Schroedinger operators: the Poeschl-Teller potential

Gestur Olafsson·Shijun Zheng
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Abstract

We address the function space theory associated with the Schroedinger operator H. The discussion is featured with the Poeschl-Teller potential in quantum physics. Using biorthogonal dyadic system, we introduce Besov spaces and Triebel-Lizorkin spaces (including Sobolev spaces) associated with H. We then use interpolation method to identify these spaces with the classical ones for a certain range of p,q> 1. A physical implication is that the corresponding wave function $ψ(t,x)=e^{-i t H }f(x)$ admits appropriate time decay in the Besov space scale.

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Gestur Olafsson, Shijun Zheng. 2005-09-27. Function spaces associated with Schroedinger operators: the Poeschl-Teller potential. https://arxiv.org/abs/math/0509642

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