Item under Review: (DE020076712)
    Author(s): Naboko, S.N.; Yanas, Ya.
Title: Criteria for semiboundedness in a class of unbounded Jacobi
operators. Source: St. Petersbg. Math J. 14, No.3, 479-485 (2003);
translation from Algebra Anal. 14, No.3, 158-168 (2002). [ISSN
1061-0022] Preassigned classification: (MSC2000) 47B36; 39A70;
47A10



A class of unbounded Jacobi operators is specified via certain
growth, smoothness and periodic-modulation requirements. Then, the
main result, viz., the criterion of semiboundedness from
below/above in the positivity/negativity of all the roots of a
certain characteristic equation is proved. Finally, a few
illustrations are added. The key idea of the paper lies in finding
a dependence of the semiboundedness property on the boundary B of
the absolutely continuous spectrum of an auxiliary matrix. In this
sense, the examples also clarify the instability of this
dependence at B=0.