On rational approximation in a ball in ℂN
We study rational approximations of elements of a special class of meromorphic functions which are characterized by their holomorphic behavior near the origin in balls in ℂN by means of their rational approximants. We examine two modes of convergence for this class: almost uniform-type convergence a...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200003616 |
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| Summary: | We study rational approximations of
elements of a special class of meromorphic functions which are
characterized by their holomorphic behavior near the origin in
balls in ℂN by means of their rational approximants. We
examine two modes of convergence for this class: almost
uniform-type convergence analogous to Montessus-type convergence
and weaker form of convergence using capacity based on the
classical Tchebychev constant. These methods enable us to
generalize and extend key results of Pommeranke and Gonchar. |
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| ISSN: | 0161-1712 1687-0425 |