On Pólya's theorem in several complex variables (Q2791819)

For a compact set \(K\) in \(\mathbb C^n\), let \(A(K)\) be ``the locally convex space of all germs of analytic functions on \(K\), equipped with the countable inductive limit topology''.NEWLINENEWLINEThe authors discuss the sharpness of ``the multivariate analogue of the Pólya's inequality'' given in [the second author, Mat. Sb., Nov. Ser. 96(138), 374--389 (1975; Zbl 0324.32009)]. In particular, the authors show that ``for the \textit{real} compact sets, the equality \textit{is attained} in the generalized Pólya inequality for some analytic functional \(f^*\in A(K)^*\)''.NEWLINENEWLINEFor the entire collection see [Zbl 1337.41001].