Solvability of the Gleason problem on a class of bounded pseudoconvex domains

Timothy G. Clos

doi:10.1007/s11785-022-01236-5

Solvability of the Gleason problem on a class of bounded pseudoconvex domains

Complex Variables 2022-08-04 v1

Authors: Timothy G. Clos

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Abstract

We show that if a bounded pseudoconvex domain satisfies the solvability of the bounded $\bar{\partial}$ problem, then the ideal of bounded holomorphic functions vanishing at a point in the domain is finitely generated. We also prove a smooth analog of the main result for bounded pseudoconvex domains with a sufficiently smooth boundary and also consider the Bergman space case.

Keywords

gleason problem bounded pseudoconvex domains bar partial problem holomorphic functions bergman space

Cite

@article{arxiv.2204.01121,
  title  = {Solvability of the Gleason problem on a class of bounded pseudoconvex domains},
  author = {Timothy G. Clos},
  journal= {arXiv preprint arXiv:2204.01121},
  year   = {2022}
}

Comments

9 pages. Comments welcome. Submitted

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