An Integral Operator into Dolbeault Cohomology

✍ Scribed by L. Barchini; M.G. Eastwood; A.R. Gover

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 658 KB
• Volume: 137
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1996.0050

✦ Synopsis

A construction is given for an integral transform from sections of a vector bundle over one manifold into Dolbeault cohomology of a (related) holomorphic vector bundle over a second manifold. It is demonstrated that the transform arises naturally in appropriate homogeneous situations where it is shown to agree with a certain representation theoretic intertwining operator due to Barchini, Knapp and Zierau. Our construction is geometric with the underlying correspondence being a double fibration of the type arising in connection with X-ray transforms. From this point of view many properties of the transform are immediate.