Publication: Direct and Inverse Results on Row Sequences of Simultaneous Padé–Faber Approximants
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Issued Date
2019-04-01
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ISSN
16605454
16605446
16605446
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2-s2.0-85062263129
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Mahidol University
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SCOPUS
Bibliographic Citation
Mediterranean Journal of Mathematics. Vol.16, No.2 (2019)
Suggested Citation
Nattapong Bosuwan, Guillermo López Lagomasino Direct and Inverse Results on Row Sequences of Simultaneous Padé–Faber Approximants. Mediterranean Journal of Mathematics. Vol.16, No.2 (2019). doi:10.1007/s00009-019-1307-0 Retrieved from: https://repository.li.mahidol.ac.th/handle/123456789/51226
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Title
Direct and Inverse Results on Row Sequences of Simultaneous Padé–Faber Approximants
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Abstract
© 2019, Springer Nature Switzerland AG. Given a vector function F= (F 1 , … , F d ) , analytic on a neighborhood of some compact subset E of the complex plane with simply connected complement, we define a sequence of vector rational functions with common denominator in terms of the expansions of the components F k , k= 1 , … , d, with respect to the sequence of Faber polynomials associated with E. Such sequences of vector rational functions are analogous to row sequences of type II Hermite–Padé approximation. We give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of the sequence of vector rational functions so constructed. The exact rate of convergence of these denominators is provided and the rate of convergence of the approximants is estimated. It is shown that the common denominators of the approximants detect the poles of the system of functions “closest” to E and their order.