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We discuss applications of the M. G. Kre\u{\i}n theory of the spectral shift function to the multi-dimensional Schr\"odinger operator as well as specific properties of this function, for example, its high-energy asymptotics. Trace identities for the Schr\"odinger operator are derived.

Оператор Шрeдингера: определители возмущения, функция спектрального сдвига, тождества следов и прочее