Asymptotics for the Approximation of Wave Functions by Exponential-Sums
نویسندگان
چکیده
منابع مشابه
On Approximation of Functions by Exponential Sums
We introduce a new approach, and associated algorithms, for the efficient approximation of functions and sequences by short linear combinations of exponential functions with complex-valued exponents and coefficients. These approximations are obtained for a finite but arbitrary accuracy and typically have significantly fewer terms than Fourier representations. We present several examples of thes...
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Bilinear Sums with Exponential Functions
Let g = 0,±1 be a fixed integer. Given two sequences of complex numbers (φm) ∞ m=1 and (ψn) ∞ n=1 and two sufficiently large integers M and N , we estimate the exponential sums ∑ p≤M gcd(ag,p)=1 ∑ 1≤n≤N φpψnep (ag ) , a ∈ Z, where the outer summation is taken over all primes p ≤ M with gcd(ag, p) = 1.
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1995
ISSN: 0021-9045
DOI: 10.1006/jath.1995.1110