Article
Ufa Mathematical Journal
Volume 4, Number 1, pp. 82-100
An almost exponential sequence of exponential polynomials
Krivosheyev A.S.
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A special sequence of exponential polynomials whose exponentials are divided into relatively small groups is studied in the article. It is proved this sequence is almost an exponential sequence for each convex domain of complex plane. With a help of this result there are obtained necessary and sufficient conditions for considered sequence to be a basis in a closed and invariant under differentiation subspace of the space of analytic functions in a convex domain. Also two methods of description of all class of bases in invariant subspace whose elements are exponential polynomials.