ON THE BOUNDARY VALUE OF BESOV-BERGMAN SPACES

1984 ◽  
Vol 10 (1) ◽  
pp. 46
Author(s):  
de Souza
Keyword(s):  
Boundary Value ◽  
Bergman Spaces

A NOTE ON TOEPLITZ OPERATORS

1996 ◽  
Vol 07 (04) ◽  
pp. 501-513 ◽  
Author(s):  
ERIK GUENTNER ◽  
NIGEL HIGSON
Keyword(s):  
Riemannian Manifolds ◽  
Toeplitz Operators ◽  
Boundary Value ◽  
Bergman Spaces ◽  
Index Theorem ◽  
Value Theory ◽  
Point Of View ◽  
Dirac Type ◽  
Complete Manifolds ◽  
Complete Riemannian Manifolds

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.

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