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

Authors : P D SRIVASTAVA

Pages : 0-0

Doi:10.1501/Commua1_0000000569

View : 38 | Download : 9

Publication Date : 1984-01-01

Article Type : Research Paper

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 00 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 insert ignore into journalissuearticles values(M ); an insert ignore into journalissuearticles values(z); = z n {1 + Xn insert ignore into journalissuearticles values(z);} where each /.n is an entire function vanishing at origin. Sufficient condi­ tions for {an } defined by insert ignore into journalissuearticles values(1.1); to be a proper Pincherle basis in T, have been established by Arsove [1].
Keywords : pincherle, space, functions

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