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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832563456015859712 |
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| author | P. W. Darko S. M. Einstein-Matthews C. H. Lutterodt |
| author_facet | P. W. Darko S. M. Einstein-Matthews C. H. Lutterodt |
| author_sort | P. W. Darko |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-cd8b8adaffc246948a86c6a6d5aedfec |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-cd8b8adaffc246948a86c6a6d5aedfec2025-02-03T01:20:15ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-0124533534410.1155/S0161171200003616On rational approximation in a ball in ℂNP. W. Darko0S. M. Einstein-Matthews1C. H. Lutterodt2Department of Mathematics, Howard University, 2441 6th Street, N. W. Washington D. C 20059, USADepartment of Mathematics, Howard University, 2441 6th Street, N. W. Washington D. C 20059, USADepartment of Mathematics, Howard University, 2441 6th Street, N. W. Washington D. C 20059, USAWe 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.http://dx.doi.org/10.1155/S0161171200003616Rational approximationmeromorphic functions Montessus-type convergenceweak convergence in capacity Tchebychev constantunisolvent rational approximation (URA)-sequences. |
| spellingShingle | P. W. Darko S. M. Einstein-Matthews C. H. Lutterodt On rational approximation in a ball in ℂN International Journal of Mathematics and Mathematical Sciences Rational approximation meromorphic functions Montessus-type convergence weak convergence in capacity Tchebychev constant unisolvent rational approximation (URA)-sequences. |
| title | On rational approximation in a ball in ℂN |
| title_full | On rational approximation in a ball in ℂN |
| title_fullStr | On rational approximation in a ball in ℂN |
| title_full_unstemmed | On rational approximation in a ball in ℂN |
| title_short | On rational approximation in a ball in ℂN |
| title_sort | on rational approximation in a ball in cn |
| topic | Rational approximation meromorphic functions Montessus-type convergence weak convergence in capacity Tchebychev constant unisolvent rational approximation (URA)-sequences. |
| url | http://dx.doi.org/10.1155/S0161171200003616 |
| work_keys_str_mv | AT pwdarko onrationalapproximationinaballincn AT smeinsteinmatthews onrationalapproximationinaballincn AT chlutterodt onrationalapproximationinaballincn |