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

DOI10.1007/S11785-022-01236-5arXiv2204.01121MaRDI QIDQ6395537

Timothy G. Clos

Publication date: 3 April 2022

Abstract: We show that if a bounded pseudoconvex domain satisfies the solvability of the bounded $$ 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.

Mathematics Subject Classification ID

Algebras of holomorphic functions of several complex variables (32A38) Domains of holomorphy (32T05)

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