An Analog of the Paley-Wiener Theorem for Entire Functions of the Space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$W _{\sigma} ^{p}, 1 < p < 2$\end{document}, and some Applications

We obtain an analogue of the well-known Paley-Wiener Theorem on integral representation of entire functions of exponential type at most σ, σ > 0, which belong to the space L2(ℝ). We choose 1 < p < 2 and σ > 0 and work in Lp (ℝ). We find optimal estimates of the modulus on any line parallel to ℝ, and present applications to best analytic continuation from a finite set in ℂ for entire functions of this class. The main result was announced in [7].