Results 271 to 280 of about 66,276 (316)

Estimates of Fourier Coefficients

gmj, 2003
Abstract Some well-known properties of the trigonometric system as well as of the Haar and Welsh systems are generalized to general orthonormal systems.
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Asymptotic Estimates of Fourier Coefficients

SIAM Journal on Mathematical Analysis, 1974
Complex variable techniques are used to estimate the Fourier coefficients of functions expanded in series of Jacobi, Laguerre and Hermite polynomials.
Elliott, David, Tuan, P. D.
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Fourier coefficients of and

The Mathematical Gazette, 2023
Recall that for a 2 π -periodic function f , the Fourier coefficients on the interval (–Π, Π) are and the Fourier series for
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On Density of Fourier Coefficients

Canadian Mathematical Bulletin, 1973
Letfbe anLintegrable real valued function of period 2π and let(1)be its Fourier series. It is known that iffis of bounded variation then allnanandnbn(n=1,2,3,…) lie in the interval [-V(F)/π, V(F)/π;] whereV(f) is the total variation off. M. Izumi and S.
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The calculation of Fourier Coefficients

SIAM Journal on Numerical Analysis, 1967
where q is a positive integer and f(x) is a real function which, together with its first 2p derivatives, is continuous in the interval [0, 1]. The method involves calculating trapezoidal rule approximationsto 1 f(t) dt with different mesh ratios and combining these results. In the case that f(x) is a periodic function with period 1, this method reduces
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Estimation of Fourier coefficients

IEEE Transactions on Instrumentation and Measurement, 1989
It is shown that the maximum-likelihood estimation or robust estimation of the Fourier coefficients may be preferable to Fourier transformation if the noise contains outliers or is otherwise not normally distributed. The reason is that, in that case, these estimators produce Fourier coefficient estimates and, therefore, system parameter estimates ...
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Fourier coefficient harmonic analyzer

Electrical Engineering, 1949
THE SEPARATION of a complex curve into its constituent sine and cosine curves of proper amplitude and phase by means of a Fourier series analysis is well known, and this method is frequently used in many branches of engineering and mathematics. All who have ever made such an analysis know that the computation for the Fourier coefficients can be very ...
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FOURIER EXPANSIONS WITH MODULAR FORM COEFFICIENTS

International Journal of Number Theory, 2009
In this paper, we study the Fourier expansion where the coefficients are given as the evaluation of a sequence of modular forms at a fixed point in the upper half-plane. We show that for prime levels l for which the modular curve X0(l) is hyperelliptic (with hyperelliptic involution of the Atkin–Lehner type) then one can choose a sequence of weight k (
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Uniform approximation by Fourier–Stieltjes coefficients

Mathematical Proceedings of the Cambridge Philosophical Society, 1968
In chapter I, E = {nk} ⊂ Z is shown to be a Sidon set if and only if (**). For each x ∈ T,.Let E ⊂ Z+ be a lacunary sequence. In chapter II, it is constructively shown that the characteristic function of E is uniformly approximable by Fourier–Stieltjes coefficients; i.e. ϕE ∈ M(T)∧−.
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Generalized Lipschitz Classes and Fourier Coefficients

Mathematical Notes, 2004
The author proves several general results. Among others he gives a criterion for a function to belong to the generalized Lipschitz class defined by using moduli of smoothness of positive orders and presents necessary and sufficient conditions for this criterion to hold.
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