Publication: Direct and inverse results for multipoint Hermite–Padé approximants
Issued Date
2019-06-01
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ISSN
1664235X
16642368
16642368
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2-s2.0-85066295309
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Mahidol University
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SCOPUS
Bibliographic Citation
Analysis and Mathematical Physics. Vol.9, No.2 (2019), 761-779
Suggested Citation
N. Bosuwan, G. López Lagomasino, Y. Zaldivar Gerpe Direct and inverse results for multipoint Hermite–Padé approximants. Analysis and Mathematical Physics. Vol.9, No.2 (2019), 761-779. doi:10.1007/s13324-019-00316-8 Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/51222
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Title
Direct and inverse results for multipoint Hermite–Padé approximants
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Abstract
© 2019, Springer Nature Switzerland AG. Given a system of functions f= (f1, … , fd) analytic on a neighborhood of some compact subset E of the complex plane with simply connected complement in the extended complex plane, we give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of row sequences of multipoint Hermite–Padé approximants under a general extremal condition on the table of interpolation points. The exact rate of convergence of these denominators is provided and the rate of convergence of the simultaneous approximants is estimated. These results allow us to detect the location of the poles of the system of functions which are in some sense closest to E.