6533b823fe1ef96bd127e989

RESEARCH PRODUCT

THE ARITHMETIC BOHR RADIUS

Andreas DefantManuel MaestreChristopher Prengel

subject

symbols.namesakeMonomialMathematics::Complex VariablesGeneral MathematicssymbolsRegular polygonHolomorphic functionHyperconeArithmeticBohr radiusBohr modelMathematics

description

We study the arithmetic Bohr radius of Reinhardt domains in ℂ n which was successfully used in our study of monomial expansions for holomorphic functions in infinite dimensions. We show that this new Bohr radius is different from the radii invented by Boas and Khavinson and Aizenberg. It gives an explicit formula for the n-dimensional hypercone (which means n-dimensional variants of classical results of Bohr and Bombieri), and moreover asymptotically corrects upper and lower estimates for various types of convex and non-convex Reinhardt domains.

yearjournalcountryeditionlanguage
2007-11-25The Quarterly Journal of Mathematics
https://doi.org/10.1093/qmath/ham028