Zero Sets Of Paley-Wiener Space

In this paper, we investigate zero sets of Paley-Wiener space, and give a complete description of zero sets for Paley-Wiener space.As an application, we discuss properties of zero sets for Paley-Wiener space. Setting A is a zero set of Paley-Wiener space,Λ1(?)Λ. We show thatΛ1 is not a zero set of Paley-Wiener space ifΛ1 is finite;Λ1 need not be a zero set of Paley-Wiener space ifΛ1 is infinite, and the union of two zero sets for Paley-Wiener space need not be a zero set of Paley-Wiener space.Finally, we construct an entire function of exponential type at mostπ, although it tends to zero on the real axis, it doesn't belong to Paley-Wiener space.