Stas Kupin
Spectral properties of Jacobi matrices and sum rules of special form
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ABSTRACT.  In this article, we relate the properties of elements of a Jacobi 
matrix from certain class to the properties of its spectral measure. 
The main tools we use are the so-called sum rules originally 
suggested by Case. 
As a corollary of the main theorem, we obtain a direct counterpart 
of a result by Molchanov-Novitskii-Vainberg for ``continuous'' 
Schr\"odinger operator.