Hörmander’s L² -Method, ∂-Problem and Polyanalytic Function Theory in One Complex Variable

Authors

Daniel Alpay, Chapman UniversityFollow
Fabrizio Colombo, Politecnico di MilanoFollow
Kamal Diki, Chapman UniversityFollow
Irene Sabadini, Politecnico di MilanoFollow
Daniele C. Struppa, Chapman UniversityFollow

Document Type

Article

Publication Date

3-27-2023

Abstract

In this paper we consider the classical ∂-problem in the case of one complex variable both for analytic and polyanalytic data. We apply the decomposition property of polyanalytic functions in order to construct particular solutions of this problem and obtain new Hörmander type estimates using suitable powers of the Cauchy-Riemann operator. We also compute particular solutions of the ∂-problem for specific polyanalytic data such as the Itô complex Hermite polynomials and polyanalytic Fock kernels.

Comments

This article was originally published in Complex Analysis and Operator Theory, volume 17, in 2023. https://doi.org/10.1007/s11785-023-01340-0

Recommended Citation

Alpay, D., Colombo, F., Diki, K. et al. Hörmander’s L²-Method, ∂-Problem and Polyanalytic Function Theory in One Complex Variable. Complex Anal. Oper. Theory 17, 41 (2023). https://doi.org/10.1007/s11785-023-01340-0

Peer Reviewed

1

Copyright

The authors

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.