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http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/7673| Title: | Determining sets for holomorphic functions on the symmetrized bidisk |
| Authors: | Das, Bata Krishna Kumar, Poornendu SAU, HARIPADA Dept. of Mathematics |
| Keywords: | Rational inner functions Symmetrized bidisk distinguished varieties Nevanlinna-Pick interpolation Uniqueness varieties Determining sets Extension problem Reproducing kernel Hilbert spaces 2023-MAR-WEEK3 TOC-MAR-2023 2023 |
| Issue Date: | Sep-2023 |
| Publisher: | Cambridge University Press |
| Citation: | Canadian Mathematical Bulletin, 66(03). |
| Abstract: | A subset D of a domain omega c C-d is determining for an analytic function f : omega-+ D if whenever an analytic function g : omega-+ D coincides with f on D, equals to f on whole omega. This note finds several sufficient conditions for a subset of the symmetrized bidisk to be determining. For any N >_ 1, a set consisting of N-2 -N + 1 many points is constructed which is determining for any rational inner function with a degree constraint. We also investigate when the intersection of the symmetrized bidisk intersected with some special algebraic varieties can be determining for rational inner functions |
| URI: | https://doi.org/10.4153/S0008439523000103 http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/7673 |
| ISSN: | 0008-4395 1496-4287 |
| Appears in Collections: | JOURNAL ARTICLES |
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