The ∂-complex on the Segal–Bargmann space
- Author(s)
- Friedrich Haslinger
- Abstract
We study certain densely defined unbounded operators on the Segal– Bargmann space. These are the annihilation and creation operators of quantum mechanics. In several complex variables we have the ∂-operator and its adjoint ∂
∗acting on (p, 0)-forms with coefficients in the Segal–Bargmann space. We consider the corresponding ∂-complex and study the spectral properties of the corresponding complex Laplacian ˜□ = ∂∂
∗ + ∂
∗∂. Finally, we study a more general complex Laplacian ˜□
D = DD
∗ + D
∗D, where D is a differential operator of polynomial type, to find the canonical solutions to the inhomogeneous equations Du = α and D
∗v = β.
- Organisation(s)
- Department of Mathematics
- Journal
- Annales Polonici Mathematici
- Volume
- 123
- Pages
- 295-317
- No. of pages
- 23
- DOI
- https://doi.org/10.4064/ap180715-2-11
- Publication date
- 2019
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101002 Analysis, 101008 Complex analysis
- Keywords
- ASJC Scopus subject areas
- General Mathematics
- Portal url
- https://ucrisportal.univie.ac.at/en/publications/8abd68e6-9826-4a33-9ac1-dadf866f4486