Let a be a sequence of points in the unit ball of Cn. Eric Amar and the author have introduced the nonnegative quantity ρ(a) = infα infk Πj:j≠k dG(αj, αk), where dG is the Gleason distance in the unit disk and the first infimum is taken over all sequences α in the unit disk which map to a by a map from the disk to the ball.
The value of ρ(a) is related to whether a is an interpolating sequence with respect to analytic disks passing through it, and if a is an interpolating sequence in the ball, then ρ(a) > 0.
In this work, we show that ρ(a) can be obtained as the limit of the same quantity for the truncated finite sequences, and that ρ(a) depends continuously on a when a is finite. Furthermore, we describe some of the behavior of the minimizing sequences of maps involved in the extremal problem used to define ρ.
@article{urn:eudml:doc:41232,
title = {Continuity and convergence properties of extremal interpolating disks.},
journal = {Publicacions Matem\`atiques},
volume = {39},
year = {1995},
pages = {335-347},
mrnumber = {MR1370890},
zbl = {0847.40003},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41232}
}
Thomas, Pascal J. Continuity and convergence properties of extremal interpolating disks.. Publicacions Matemàtiques, Tome 39 (1995) pp. 335-347. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41232/