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Momentum Operators in Two Intervals: Spectra and Phase Transition
Authors:Palle E. T. Jorgensen  Steen Pedersen  Feng Tian
Affiliation:1. Department of Mathematics, The University of Iowa, Iowa City, IA, 52242-1419, USA
2. Department of Mathematics, Wright State University, Dayton, OH, 45435, USA
Abstract:We study the momentum operator defined on the disjoint union of two intervals. Even in one dimension, the question of two non-empty open and non-overlapping intervals has not been worked out in a way that extends the cases of a single interval and gives a list of the selfadjoint extensions. Starting with zero boundary conditions at the four endpoints, we characterize the selfadjoint extensions and undertake a systematic and complete study of the spectral theory of the selfadjoint extensions. In an application of our extension theory to harmonic analysis, we offer a new family of spectral pairs. Compared to earlier studies, it yields a more direct link between spectrum and geometry.
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