We prove some finiteness theorems for continuous (respectively, differential) operators that intertwine two induced representations of a reductive Lie group and a reductive subgroup. We then extend the 'F-method' from local to non-local operators, aiming for detailed analysis of such operators. We illustrate this general idea by concrete examples in conformal geometry, and explain how we can discover functional equations among such operators by the F-method. We also indicate how continuous operators with meromorphic parameters yield conformally equivariant differential operators as residues.
© Toshiyuki Kobayashi