
handle: 11693/50651 , 11693/24804 , 11693/24243
A real Paley-Wiener function (PW-function) is an entire function, \(f\), of exponential type such that \(f\in L_2(\mathbb R)\) and \(f(\mathbb R)\subset \mathbb R\). J. R. Higgins posed the question whether or not some derivative of an arbitrary real Paley-Wiener function has infinitely many real zeros. In this interesting paper, the authors construct a wide class of real PW-functions, \(f\), with the property that each derivative, \(f^{(n)}\), \(n=0,1,2\dots\), has only a finite number of real zeros. Moreover, they obtain a result (Theorem 2) which gives a sharp asymptotic estimate (as \(n\to\infty\)) of the length of the smallest interval which contains all the real zeros of \(f^{(n)}\).
Levy theorem., Special classes of entire functions of one complex variable and growth estimates, oscillation, rate of decay, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Entire functions of one complex variable (general theory), real zeros, Paley-Wiener functions, derivatives, zeros, Fourier transform, real Paley-Wiener functions
Levy theorem., Special classes of entire functions of one complex variable and growth estimates, oscillation, rate of decay, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Entire functions of one complex variable (general theory), real zeros, Paley-Wiener functions, derivatives, zeros, Fourier transform, real Paley-Wiener functions
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