Sub-Dirac operators, spectral Einstein functionals and the noncommutative residue

In this paper, we define the spectral Einstein functional associated with the sub-Dirac operator for manifolds with boundary. A proof of the Dabrowski-Sitarz-Zalecki type theorem for spectral Einstein functions associated with the sub-Dirac operator on four-dimensional manifolds with boundary is also given.
Comment: arXiv admin note: text overlap with arXiv:2308.00833, arXiv:2312.00838