2024/10/29 by Knese, Greg · 1 citation
#32A35 #32A38 #47A13 #47A48 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2410.21693
This article examines three radii associated to bounded analytic functions on the polydisk: the well-known Bohr radius, the Bohr-Agler radius, and the Schur-Agler radius. We prove explicit upper and lower bounds for the Bohr-Agler radius, an explicit lower bound for the Schur-Agler radius, and an asymptotic upper bound for the Schur-Agler radius. The Bohr-Agler radius obeys the same (known) asymptotic as the Bohr radius while we show the Schur-Agler radius is roughly of the same growth as the Bohr radius. As a corollary, we bound the Bohr radius on the bidisk below by 0.3006. Finally, we improve some estimates of P.G. Dixon on Agler norms of homogeneous polynomials using some modern inequalities.