A quaternionic analogue of the Segal-Bargmann transform. (English) Zbl 1364.44002
Authors’ summary: The Bargmann-Fock space of slice hyperholomorphic functions was recently introduced by Alpay, Colombo, Sabadini and Salomon. In this paper, we reconsider this space and present a direct proof of its independence of the slice. We also introduce a quaternionic analogue of the classical Segal-Bargmann transform and discuss some of its basic properties. The explicit expression of its inverse is obtained, and the connection to the left one-dimensional quaternionic Fourier transform is given.
Reviewer: Kun Soo Chang (Seoul)
MSC:
| 44A15 | Special integral transforms (Legendre, Hilbert, etc.) |
| 30H20 | Bergman spaces and Fock spaces |
| 32A17 | Special families of functions of several complex variables |
| 32A10 | Holomorphic functions of several complex variables |
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
Keywords:
slice regular functions; slice hyperholomorphic Bargmann-Fock space; quaternionic Segal-Bargmann transform; left one-dimensional quaternionic Fourier transformReferences:
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