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In this paper, we define the spectral Einstein functional associated with thesub-signature operator for manifolds with boundary. Motivated by the spectralEinstein functional and the sub-signature operator, we relate them to thenoncommutative residue for manifolds with boundary. And we give the proof ofthe Dabrowski-Sitarz-Zalecki type theorems for the spectral Einstein functionalassociated with the sub-signature operator on 4-dimensional manifolds withboundary.

Sub-signature operators and the Dabrowski-Sitarz-Zalecki type theorems for manifolds with boundary