We consider the quotient module Q of the Hardy module H2(S) defined by an analytic set M ̃ satisfying certain conditions. Denote d = dimCM ̃ . Solving a previously- raised problem, we show that certain 2d-antisymmetric sums of module operators are in the trace class. In the case d = 1, we derive a trace formula on Q, which answers another previously-raised question.

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