Results 211 to 220 of about 84,599 (243)

Exponential estimates for the maximum of partial sums. I

Acta Mathematica Hungarica, 1979
F Mòricz
exaly   +3 more sources

On the Problem of Parameter Estimation in Exponential Sums

Constructive Approximation, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Filbir, F., Mhaskar, H. N., Prestin, J.
openaire   +1 more source

An Estimate of a Special Exponential Sum

Mathematische Nachrichten, 1986
The exponential sums \(\sum^{n}_{k=1}k^{2\pi ir}\), \(\sum^{\infty}_{k=1}k^{2\pi ir} e^{-k^ 2/n}\), and \(\sum^{n}_{k=1}k^{2\pi ir-1}\) are considered. These are closely related to Riemann's zeta-function (though the zeta-function is not mentioned in the paper), and the main results of the paper are either well-known from the theory of the zeta ...
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Estimates for exponential sums. Applications

Journal of Mathematical Sciences, 2012
We obtain estimates of exponential (in particular, trigonometric) sums in terms of rational functions. Examples of sharp inequalities are given. These inequalities are used for estimating solutions to linear homogeneous differential equations with constant coefficients.
V. I. Danchenko, A. E. Dodonov
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An estimate of theL 1-norm of an exponential sum

Mathematical Notes, 1996
The following theorem is proved. Suppose that \(A\geq 1/2\), \(10\) the inequality \[ \int_0^1 \Biggl| \sum_{n=1}^N \alpha_n \exp(2\pi ixf(n)) \Biggr| dx\geq \exp(2^{-15} A^{-2} (\log N)^{3-2\beta}) \] is valid. This improves an estimate of S. V. Bochkarev. The proof uses an estimate of a trigonometric sum due to O. V. Popov.
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Estimates on polynomial exponential sums

Israel Journal of Mathematics, 2010
Let \(f(x)=a_1x^{k_1}+\cdots+a_rx^{k_r}\in \mathbb{Z}[x]\) be a polynomial of degree \(d\), and let \(q\) be a positive integer. Assume \((a_1,\cdots,a_r,q)=1\), and define \(e_q(x)=e^{2\pi i \frac{x}{q}}\). This paper estimates exponential sums of the form \[ \sum_{1\leq x< q;~(x,q)=1}e_q(f(x)) \quad \text{and}\quad \sum_{1\leq x\leq q}e_q(f(x ...
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Lp norm local estimates for exponential sums

Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2000
The authors announce the proof of the following theorem: For every real number \(p>1\) there is an explicitly computable constant \(K_p> 0\) such that, for any arc \(J\) of the one-dimensional torus \(\mathbb{T}= \mathbb{R}/\mathbb{Z}\) with \(|J|> 0\), no matter how small, one can find some exponential sum \(f(x)= \sum_{k=1}^m \exp(2i\pi N_kx)\) (the \
Anderson, Bruce, Ash, J. Marshall, Jones, Roger L., Rider, Daniel G., Saffari, Bahman   +4 more
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Estimate for exponential sums and its applications

Frontiers of Mathematics in China, 2012
Let \(f_{k}(n)\) be the characteristic function of \(n\) with \(\Omega(n)=k\), and \[ T_{k}(x,\alpha)=\sum_{n\leq x}f_{k}(n)e(n\alpha). \] Write \[ r(N)=\#\{N=f_{k}(n_{1})n_{1}+f_{k}(n_{2})n_{2}+f_{k}(n_{3})n_{3}\}. \] The author obtains the following result: Let \(k\leq (\log\log N)^{1-\Delta}\), then \[ r(N)=\frac{1}{2}N^{2}\mathfrak{S}(N)(\frac ...
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Glottal source estimation using a sum of exponentials model

The Journal of the Acoustical Society of America, 1989
This paper describes an algorithm for simultaneously estimating the parameters of a model for the glottal source and the vocal tract filter. The glottal source signal is described by t.he four-parameter LF model [Fant et al., Speech Transmis. Lab. Q. Prog. Stat. Rep. (1984)].
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On Hua's Estimate for Exponential Sums

Journal of the London Mathematical Society, 1982
Loxton, John H., Smith, Robert A.
openaire   +2 more sources