A generalization of universal Taylor series in simply connected domains

作者：Tsirivas N^*

来源：Journal of Mathematical Analysis and Applications, 2012, 388(1): 361-369.

DOI：10.1016/j.jmaa.2011.11.038

• Universal series
• Cesaro hypercyclicity
• Universality
• Hypercyclicity
• Bernstein-Walsh Theorem
• Seleznev Theorem

Let Omega be a simply connected proper subdomain of the complex plane and z(0) be a point in Omega. It is known that there are holornorphic functions f on Omega for which the partial sums (Sn(f, z(0))) of the Taylor series about z(0) have universal approximation properties outside 12. In this paper we investigate what can be said for the sequence (beta(n)S(n)(f, z(0))) when (beta(n)) is a sequence of complex numbers. We also study a related analogue of a classical theorem of Seleznev concerning the case where the radius of convergence of the universal power series is zero.

• 出版日期2012-4-1