We study Toeplitz operators on Bergman spaces using techniques from the analysis of Dirac-type operators on complete Riemannian manifolds, and prove an index theorem of Boutet de Monvel from this point of view. Our approach is similar to that of Baum and Douglas [2], but we replace boundary value theory for the Dolbeaut operator with much simpler estimates on complete manifolds.
We identify a class of Dirac-Schrodinger operators on in- complete manifolds and show that the index theory of these operators, including its expression in K homology, is parallel to that of Dirac-Schrodinger operators on complete manifolds.
Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights.