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Session III.7 - Special Functions and Orthogonal Polynomials


Rate of Pole Detection Using Pad\'{e} Approximants to Polynomial Expansions

Nattapong Bosuwan

Mahidol University , Thailand   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Pad\'{e} approximation and its generalizations were proved to be useful tools in localization of singularities of functions. In this work, we investigate the rate of detection of poles using orthogonal Pad\'{e} and Pad\'{e}-Faber approximations. We provide global estimates on this rate of detection and show that our global estimates are sharp. Our results in this paper serve as an analogue of the direct part of Gonchar's theorem in 1981 for such Pad\'{e} approximants.

Joint work with Methawee Wajasat (Mahidol University).

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