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absolutely integrable Analytic Continuation apply Lemma 1.2 approximated arbitrarily arbitrary interval arbitrary sum assertion follows Beurling bounded linear functional boundedness property Chapter characteristic function compact support concave function consequently Consider an arbitrary Consider an interval convergence Corollary definition denote eA(f easily seen existence exponential EXPONENTIAL POLYNOMIALS f is mean-periodic finite interval finite number following lemma follows from Lemma formula fºs Fourier transform function f Hahn–Banach theorem harmonic and regular harmonic transform holomorphic inequality integer integral equation 1.9 interpolation is possible Kahane 9 kNri Laplace transforms le=inf linear vector space Mean-periodic Function metric Nordlander norms notion Paley and Wiener pelº polynomial positive numbers proof is complete pseudo-periodic real number regular everywhere satisfies Schwartz's semi-regular sequence ſexp ſlog log Suppose that f Theorem 2.2 tion transform of f translations uniformly upper density zero