Entire Functions of Bounded Index
نویسنده
چکیده
Since this series is absolutely convergent everywhere in the plane, the terms \an\ must approach 0. Consequently, there exists for each a, an index n0 = n(a) ior which \an\ is a maximal coefficient. B. Lepson [2] raised the problem of characterizing entire functions for which n(a) is bounded. The latter are called functions of bounded index. In what follows, we shall give a partial solution to Lepson's problem. We shall also include a number of results using somewhat different conditions than those suggested by Lepson.
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