Opuscula Math. 35, no. 2 (2015), 199-234

Opuscula Mathematica

Decisiveness of the spectral gaps of periodic Schrödinger operators on the dumbbell-like metric graph

Hiroaki Niikuni

Abstract. In this paper, we consider periodic Schrödinger operators on the dumbbell-like metric graph, which is a periodic graph consisting of lines and rings. Let one line and two rings be in the basic period. We see the relationship between the structure of graph and the band-gap spectrum.

Keywords: quantum graph, spectral gap, band structure, Hill operator.

Mathematics Subject Classification: 34L05, 34L15, 34B45.

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  • Hiroaki Niikuni
  • Maebashi Institute of Technology, 460-1 Kamisadori, Maebashi City, Gunma, 371-0816, Japan
  • Communicated by P.A. Cojuhari.
  • Received: 2014-05-23.
  • Revised: 2014-07-22.
  • Accepted: 2014-07-26.
  • Published online: 2014-11-18.
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Cite this article as:
Hiroaki Niikuni, Decisiveness of the spectral gaps of periodic Schrödinger operators on the dumbbell-like metric graph, Opuscula Math. 35, no. 2 (2015), 199-234, http://dx.doi.org/10.7494/OpMath.2015.35.2.199

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