The main result in this paper is a one term Szego type asymptotic formulawith a sharp remainder estimate for a class of integral operators of thepseudodifferential type with symbols which are allowed to be non-smooth ordiscontinuous in both position and momentum. The simplest example of suchsymbol is the product of the characteristic functions of two compact sets, onein real space and the other in momentum space. The results of this paper areused in a study of the violation of the area entropy law for free fermions in[18]. This work also provides evidence towards a conjecture due to HaroldWidom.
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