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On polynomial approximation of entire functions with index-pair \((p,q)\). (English) Zbl 1064.30034

Let \(C (E)\) be the algebra of analytic function on the set \(E.\)
The authors have characterized \((p, q)\)-order and lower \((p, q)\)-type in terms of approximation errors. They have given the conditions for \(f \in C (E)\) to be extended to an entire function of regular \((p, q)\)-growth with respect to a proximate order.

MSC:

30E10 Approximation in the complex plane
30D20 Entire functions of one complex variable (general theory)
52A38 Length, area, volume and convex sets (aspects of convex geometry)
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