Density of states of Jacobi matrices with periodic and asymptotically periodic coefficients

2015 ◽  
Vol 143 (12) ◽  
pp. 5293-5306 ◽  
Author(s):  
A. Bourget ◽  
T. M. Goode
Keyword(s):  
Density Of States ◽  
Jacobi Matrices ◽  
Periodic Coefficients ◽  
Asymptotically Periodic

A TRACE FORMULA FOR A FAMILY OF JACOBI OPERATORS

2009 ◽  
Vol 07 (02) ◽  
pp. 115-130 ◽  
Author(s):  
ALFONSO F. AGNEW ◽  
ALAIN BOURGET
Keyword(s):  
Differential Equation ◽  
Asymptotic Expansion ◽  
Density Of States ◽  
Trace Formula ◽  
Jacobi Matrices ◽  
Jacobi Operators ◽  
Leading Term

In this paper, we compute the leading term in the asymptotic expansion of the trace of a family of Jacobi matrices as their order gets arbitrarily large. We then apply this formula to compute the density of states of the zeros of a class of polynomials associated with the Heun differential equation.

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