Continuity and convergence properties of extremal interpolating disks.

Título inglés Continuity and convergence properties of extremal interpolating disks.
Título español Propiedades de continuidad y convergencia de discos de interpolación extremal.
Autor/es Thomas, Pascal J.
Organización UFR Math. Informat. Gest. Univ. Paul Sabatier, Toulouse, Francia
Revista 0214-1493
Publicación 1995, 39 (2): 335-347, 6 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés 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 dGj, 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.
Clasificación UNESCO 120210
Palabras clave español Funciones analíticas ; Funciones de variación acotada ; Bola unidad ; Conjuntos de interpolación ; Función entera
Código MathReviews MR1370890
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