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Some aspects of weakly pseudoconvex domains. (English) Zbl 0747.32006
Several complex variables and complex geometry, Proc. Summer Res. Inst., Santa Cruz/CA (USA) 1989, Proc. Symp. Pure Math. 52, Part 1, 199-231 (1991).
[For the entire collection see Zbl 0732.00007.]
This is a survey paper about recent results in the study of bounded pseudoconvex domains with smooth boundary. The author considers the following problems: exhaustion functions, Stein neighborhood basis, spectrum of algebras of holomorphic functions, type and $$\overline\partial$$-Neuman problem, peak functions, $$\overline\partial$$- problems and approximation.
Many unsolved problems are raised.

##### MSC:
 32T99 Pseudoconvex domains 32W05 $$\overline\partial$$ and $$\overline\partial$$-Neumann operators
##### Keywords:
pseudoconvex domain; smooth boundary; survey
Zbl 0732.00007