A note on the limiting distribution of the zeros of Padé approximants for some classes of functions

AbstractIn the present paper, we deal with functions f(z) := ∑∞n=0 anzn whose coefficients satisfy a special smoothness condition. Theorems concerning the asymptotic behaviour as n → ∞, m-fixed, of the normalized in an appropriate way Padé approximants πn,m are provided. As a consequence, results concerning the limiting distribution of the zeros are deduced

Applied Complex and Quaternionic Approximation

Quaderno del Seminario di Topologia Algebrica e Differenziale del Dipartimento di Matematica "G. Castelnuovo", Universita' di Roma "La Sapienza", Roma, Giugno 200

An analogue of Montel's theorem to some rational approximating functions

In the present paper, we consider families of rational approximants with an unbounded number of the finite poles, analytic in a domain and not taking a given complex value in this domain. Under additional conditions, we establish the normality of these sequences. (orig.)Available from TIB Hannover: RO 1945(325) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman