# Continuity and convergence properties of extremal interpolating disks.

Publicacions Matemàtiques (1995)

- Volume: 39, Issue: 2, page 335-347
- ISSN: 0214-1493

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topThomas, Pascal J.. "Continuity and convergence properties of extremal interpolating disks.." Publicacions Matemàtiques 39.2 (1995): 335-347. <http://eudml.org/doc/41232>.

@article{Thomas1995,

abstract = {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.},

author = {Thomas, Pascal J.},

journal = {Publicacions Matemàtiques},

keywords = {Funciones analíticas; Funciones de variación acotada; Bola unidad; Conjuntos de interpolación; Función entera; continuity; convergence; extremal-interpolating disks; sequence of points; unit ball; Gleason distance; unit disk; interpolating sequence; analytic disks; sequences of maps; extremal problem},

language = {eng},

number = {2},

pages = {335-347},

title = {Continuity and convergence properties of extremal interpolating disks.},

url = {http://eudml.org/doc/41232},

volume = {39},

year = {1995},

}

TY - JOUR

AU - Thomas, Pascal J.

TI - Continuity and convergence properties of extremal interpolating disks.

JO - Publicacions Matemàtiques

PY - 1995

VL - 39

IS - 2

SP - 335

EP - 347

AB - 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.

LA - eng

KW - Funciones analíticas; Funciones de variación acotada; Bola unidad; Conjuntos de interpolación; Función entera; continuity; convergence; extremal-interpolating disks; sequence of points; unit ball; Gleason distance; unit disk; interpolating sequence; analytic disks; sequences of maps; extremal problem

UR - http://eudml.org/doc/41232

ER -

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