Russian Journal of Mathematical Physics

, Volume 23, Issue 1, pp 19–34 | Cite as

Creation of spectral bands for a periodic domain with small windows

  • D. I. Borisov


We consider a Schrödinger operator in a periodic system of strip-like domains coupled by small windows. As the windows close, the domain decouples into an infinite series of identical domains. The operator similar to the original one, and defined on one copy of these identical domains, has an essential spectrum. We show that once there is a virtual level at the threshold of this essential spectrum, the windows turn this virtual level into the spectral bands for the original operator. We study the structure and the asymptotic behavior of these bands.


Spectral Band Nontrivial Solution Essential Spectrum Periodicity Cell Small Window 
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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Institute of Mathematics CC USC RAS & Bashkir State PedagogicalUniversity & University of Hradec KrálovéKrálovéCzekh

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