markov constant
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2021 ◽  
Vol 36 (2) ◽  
pp. 74-79
Author(s):  
N.Sh. Zagirov ◽  
◽  
T.U. Gadzhieva ◽  
Keyword(s):  

2019 ◽  
Vol 34 (1) ◽  
pp. 61-66
Author(s):  
N.Sh. Zagirov ◽  
◽  
T.U. Gadzhieva ◽  
Keyword(s):  

2018 ◽  
Vol 33 (3) ◽  
pp. 54-61
Author(s):  
N.Sh. Zagirov ◽  
◽  
T.U. Gadzhieva ◽  

2016 ◽  
Vol 49 (15) ◽  
pp. 155201 ◽  
Author(s):  
Edita Pelantová ◽  
Štěpán Starosta ◽  
Miloslav Znojil
Keyword(s):  

2007 ◽  
Vol 143 (1) ◽  
pp. 185-199
Author(s):  
KAZUSHI YOSHITOMI

AbstractWe study the spectral gaps of the Schrödinger operatorwhere κ∈(0,2π) and$\beta_{1},\beta_{2}\in{\mathbb R}\setminus\{0\}$are parameters. Let τ=2π−κ. Suppose that the ratio κ0:=τ/κ is irrational. We denote thejth gap of the spectrum ofHbyGj, its length by |Gj|. We obtain a relationship between the asymptotic behaviour of |Gj| asj→∞ and the Diophantine properties of κ0. In particular, we show that if β1+β2=0, thenwhereM(κ0) stands for the Markov constant of κ0.


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