Publication: On the boundedness of poles of generalized Padé approximants
Issued Date
2019-12-01
Resource Type
ISSN
16871847
16871839
16871839
Other identifier(s)
2-s2.0-85064336560
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Mahidol University
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SCOPUS
Bibliographic Citation
Advances in Difference Equations. Vol.2019, No.1 (2019)
Suggested Citation
Nattapong Bosuwan On the boundedness of poles of generalized Padé approximants. Advances in Difference Equations. Vol.2019, No.1 (2019). doi:10.1186/s13662-019-2081-9 Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/51192
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Title
On the boundedness of poles of generalized Padé approximants
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Abstract
© 2019, The Author(s). Given a function F holomorphic on a neighborhood of some compact subset of the complex plane, we prove that if the zeros of the denominators of generalized Padé approximants (orthogonal Padé approximants and Padé–Faber approximants) for some row sequence remain uniformly bounded, then either F is a polynomial or F has a singularity in the complex plane. This result extends the known one for classical Padé approximants. Its proof relies, on the one hand, on difference equations where their coefficients relate to the coefficients of denominators of these generalized Padé approximants and, on the other hand, on a curious property of complex numbers.