Título inglés | Continuity and convergence properties of extremal interpolating disks. |
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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
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. |
Clasificación UNESCO | 120210 |
Palabras clave español | Funciones analíticas ; Funciones de variación acotada ; Bola unidad ; Conjuntos de interpolación ; Función entera |
Código MathReviews | MR1370890 |
Acceso al artículo completo |