Interpolation for Entire Functions of Exponential Type and a Related Trigonometric Moment Problem
نویسندگان
چکیده
A classical theorem of Hausdorff-Young shows that when 1 < p < 2, the system of equations rp(n) = cn (-oo < n < oo) admits a solution <p in Lq{~tt,<tt) whenever {c„} E /', Here, as usual, <p denotes the complex Fourier transform of <p and q is the conjugate exponent given by p~l + q~l = 1. The purpose of this note is to show that if a set {Xn} of real or complex numbers is "sufficiently close" to the integers, then the corresponding system <p(\,) = cn is also solvable for <p whenever (c„) G lp. The proof is accomplished by establishing a similar interpolation theorem for a related class of entire functions of exponential type.
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