Geodesic
Sets of interpolation and sampling for weighted Banach spaces of holomorphic functions
Paweł Domański1 ; Mikael Lindström2
1Faculty of Mathematics and Computer Science A. Mickiewicz University and Institute of Mathematics Polish Academy of Sciences Poznań Branch Umultowska 87 61-614 Poznań, Poland
2Department of Mathematics Department of Mathematics Åbo Akademi University FIN-20500 Åbo, Finland
Annales Polonici Mathematici, Tome 79 (2002) no. 3, pp. 233-264
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We give an elementary approach which allows us to evaluate Seip's conditions characterizing interpolating and sampling sequences in weighted Bergman spaces of infinite order for a wide class of weights depending on the distance to the boundary of the domain. Our results also give some information on cases not covered by Seip's theory. Moreover, we obtain new criteria for weights to be essential.
DOI : 10.4064/ap79-3-3
Keywords: elementary approach which allows evaluate seips conditions characterizing interpolating sampling sequences weighted bergman spaces infinite order wide class weights depending distance boundary domain results information cases covered seips theory moreover obtain criteria weights essential

Paweł Domański  1   ; Mikael Lindström  2

1 Faculty of Mathematics and Computer Science A. Mickiewicz University and Institute of Mathematics Polish Academy of Sciences Poznań Branch Umultowska 87 61-614 Poznań, Poland
2 Department of Mathematics Department of Mathematics Åbo Akademi University FIN-20500 Åbo, Finland 
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     title = {Sets of interpolation and sampling
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Paweł Domański; Mikael Lindström. Sets of interpolation and sampling
 for weighted Banach spaces of holomorphic functions. Annales Polonici Mathematici, Tome 79 (2002) no. 3, pp. 233-264. doi: 10.4064/ap79-3-3

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