Convergence of generalized Nevanlinna functions
Let K be a positive integer. A sequence (/ n ) of generalized Nevanlinna functions of the class N« , which converges locally uniformly on some nonempty open subset of the complex plane to a function / , need not converge on any larger set, and / can belong to any class with 0 < K' < K. In...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2011
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| Sorozat: | Acta scientiarum mathematicarum
77 No. 3-4 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16396 |
| Tartalmi kivonat: | Let K be a positive integer. A sequence (/ n ) of generalized Nevanlinna functions of the class N« , which converges locally uniformly on some nonempty open subset of the complex plane to a function / , need not converge on any larger set, and / can belong to any class with 0 < K' < K. In this note we show that if it is a priori known that / belongs to the same class N K then the sequence (f n ) converges locally uniformly on the set (C\R)flhol/, and the sets of poles or generalized poles of nonpositive type of fn converge to the set of poles or generalized poles of nonpositive type of / . Moreover, a compactness result for generalized Nevanlinna functions is proved. |
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| Terjedelem/Fizikai jellemzők: | 425-437 |
| ISSN: | 0001-6969 |