Limit Curves for Zeros of Sections of Exponential Integrals
نویسندگان
چکیده
منابع مشابه
Zeros of Exponential Sums and Integrals
It is of frequent occurrence in problems of both pure and applied mathematics that certain values sought may be specified and must be determined as the roots of a tran-scendental equation. In particular, the equation may be of the class in which the unknown is involved only through the medium of exponential or trigonometric functions, with coefficients which are power functions or essentially s...
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We derive the large n asymptotics of zeros of sections of a generic exponential sum. We divide all the zeros of the nth section of the exponential sum into “genuine zeros,” which approach, as n → ∞, the zeros of the exponential sum, and “spurious zeros,” which go to infinity as n → ∞. We show that the spurious zeros, after scaling down by the factor of n, approach a “rosette,” a finite collecti...
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The Eneström-Kakeya theorem (the absolute value of any zero of a0+a1x+· · ·+akx, ai ∈ R is at most max( a0 a1 , a1 a2 , . . . , ak−1 ak ) ) implies |νj| ≤ k . It was shown by Szegö [8] that the numbers νj k cluster around the simple closed curve Γ = {z : |ze1−z| = 1, |z| ≤ 1} as k → ∞ and conversely each point of the Szegö curve is a limit point of the normalized zeros. Moreover Szegö [8] and a...
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ژورنال
عنوان ژورنال: Constructive Approximation
سال: 2014
ISSN: 0176-4276,1432-0940
DOI: 10.1007/s00365-014-9241-7