Proper pincherle bases in the space of entire functions having fast growth

Year 1984, Volume: 33 , - , 01.01.1984

P. D. Srıvastava

https://doi.org/10.1501/Commua1_0000000569

Abstract

1. A classical problem of fundamental interest is to study the representability of analytic functions as infinite series in a given sequ- ence of functions. In other vvords, the expansion problem in the space of entire functions T is just the problem of determining conditions under
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whiclı sequence {an } of entire functions in T constitutes a basis n=o for the space. Considerable interest attaches to the bases functions known as Pincherle bases, of the form (M ) an (z) = z n {1 + Xn (z)} where each /.n is an entire function vanishing at origin. Sufficient condi­ tions for {an } defined by (1.1) to be a proper Pincherle basis in T, have been established by Arsove [1].

Keywords

pincherle, space, functions

References

• Communications, Series A1:Mathematics and Statistics