Published April 2021
| Submitted + Published
Journal Article
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Remarks on periodic Jacobi matrices on trees
Chicago
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Abstract
We look at periodic Jacobi matrices on trees. We provide upper and lower bounds on the gap of such operators analogous to the well-known gap in the spectrum of the Laplacian on the upper half-plane with a hyperbolic metric. We make some conjectures about antibound states and make an interesting observation for the so-called rg-model where the underlying graph has r red and g green vertices and where any two vertices of different colors are connected by a single edge.
Additional Information
© 2021 Published under license by AIP Publishing. Submitted: 18 October 2020; Accepted: 19 March 2021; Published Online: 13 April 2021. J.S.C. and M.Z. would like to thank F. Harrison and E. Mantovan for the hospitality of Caltech where some of this work was done. This work was partially supported by the Swedish Research Council (VR) under Grant No. 2018-03500 (J.S.C.), the NSF grant, No. DMS-1665526 (B.S.), and the Simons Foundation grant, No. CGM-581256 (M.Z.). Data Availability: Data sharing is not applicable to this article as no new data were created or analyzed in this study.Attached Files
Published - 042101_1_online.pdf
Submitted - 2010-01701.pdf
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042101_1_online.pdf
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Additional details
- Eprint ID
- 108807
- Resolver ID
- CaltechAUTHORS:20210423-080608586
- Swedish Research Council
- 2018-03500
- NSF
- DMS-1665526
- Simons Foundation
- CGM-581256
- Created
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2021-04-23Created from EPrint's datestamp field
- Updated
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2023-10-03Created from EPrint's last_modified field