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arXiv · 1110.5948

Momentum Operators in Two Intervals: Spectra and Phase Transition

Palle E. T. Jorgensen·Steen Pedersen·Feng Tian
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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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BibTeXRIS

Palle E. T. Jorgensen, Steen Pedersen, Feng Tian. 2011-10-26. Momentum Operators in Two Intervals: Spectra and Phase Transition. https://doi.org/10.1007/s11785-012-0234-x

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