Periodic Jacobi operator with finitely supported perturbations

We describe the spectral properties of the Jacobi operator $(Hy)_n= a_{n-1} y_{n-1}+a_{n}y_{n+1}+b_ny_n,$ $n\in\Z,$ with $a_n=a_n^0+ u_n,$ $b_n= b_n^0+ v_n,$ where sequences $a_n^0>0,$ $b_n^0\in\R$ are periodic with period $q$, and sequences $u_n,$ $v_n$ have compact support. In the case $u_n\equiv 0$ we obtain the asymptotics of the spectrum in the limit of small perturbations $v_n.$

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