Distribution of the zeros of Padé polynomials and analytic continuation

S. P. Suetin

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 70 (2015) no. 5, pp. 901-951

Résumé

The problem of analytic continuation of a multivalued analytic function with finitely many branch points on the Riemann sphere is discussed. The focus is on Padé approximants: classical (one-point) Padé approximants, multipoint Padé approximants, and Hermite–Padé approximants. The main result is a theorem on the distribution of zeros and the convergence of the Hermite–Padé approximants for a system $[1,f,f^2]$, where $f$ is a multivalued function in the so-called Laguerre class $\mathscr{L}$. Bibliography: 128 titles.

Détail

Keywords: analytic continuation, continued fractions, distribution of zeros, GRS-method, convergence in capacity.
Mots-clés : orthogonal polynomials, rational approximants, Padé polynomials, Hermite–Padé polynomials

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