Journal article
Momentum Operators in Two Intervals: Spectra and Phase Transition
Complex Analysis and Operator Theory, Vol.7(6), pp.1735-1773
12/2013
DOI: 10.1007/s11785-012-0234-x
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.
Details
- Title: Subtitle
- Momentum Operators in Two Intervals: Spectra and Phase Transition
- Creators
- Palle Jorgensen - Department of Mathematics The University of Iowa Iowa City IA 52242-1419 USASteen Pedersen - Department of Mathematics Wright State University Dayton OH 45435 USAFeng Tian - Department of Mathematics Wright State University Dayton OH 45435 USA
- Resource Type
- Journal article
- Publication Details
- Complex Analysis and Operator Theory, Vol.7(6), pp.1735-1773
- DOI
- 10.1007/s11785-012-0234-x
- ISSN
- 1661-8254
- eISSN
- 1661-8262
- Publisher
- Springer Basel; Basel
- Language
- English
- Date published
- 12/2013
- Academic Unit
- Mathematics
- Record Identifier
- 9983985864502771
Metrics
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