Interpolation series expansions in spaces $W_{s + 1/2,\sigma }^{p,w}$ of entire functions

Abstract

In this chapter we establish some theorems relating to interpolation series expansions of entire functions Φ(z) of order s +1/2 (where s ≥ 1 is an arbitrary natural number) and of type ≤ σ,which are of spaces $W_{s+1/2,\sigma}^{p,w}$ ,i.e. for which

$$ {\left\{{\sum\limits_{j=-8}^8{\int_0^{+\infty}{\left|\Phi\right.}}\left({r{e^{ixj(8+1/2)}}}\right)\left|{^p}\right.{r^w}dr}\right\}^{1/p}}<+\infty $$

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