Results 261 to 270 of about 1,311,043 (300)

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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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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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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The Möbius inversion and Fourier coefficients

Applied Mathematics and Computation, 2001
The authors show that an analogue of the Möbius inversion formula in a commutative semigroup with unique factorization can be used to study \(n\)-dimensional Fourier coefficients. The authors utilize to this aim an arbitrary algebraic number field of degree \(n\), whose ring of integers is a unique factorization domain.
Zhao-Dou Chen, Yanan Shen, Jun Ding
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On the Order of Magnitude of Fourier Coefficients

SIAM Journal on Mathematical Analysis, 1986
Let f(t) be of period 2, f(t)\(\in L(-1,1)\). Let its Fourier cosine and sine coefficients be respectively \(a_ m,b_ n\). It is familiar that \(a_ n\to 0\), \(b_ n\to 0\) as \(n\to \infty\). Even if we restrict ourselves to the case in which f(t) is continuous, these results are best possible in the sense that, given any sequence \(\{k_ n\}\) with ...
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Instability Phenomena for the Fourier Coefficients

Mathematische Nachrichten, 1996
AbstractLet P be an elliptic differential operator on a non‐compact connected manifold X; suppose that both X and the coefficients of P are real analytic. Given a pair of open sets D and σ in X with σ⊂⊂ D ⊂⊂ X, we fix a sequence {ev} of solutions of Pu = 0 in D which are pairwise orthogonal under integration over both D and σ. By orthogonality is meant
Aizenberg, Lev, Tarkhanov, Nikolai
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ON A THEOREM OF BELLMAN ON FOURIER COEFFICIENTS

Russian Academy of Sciences. Sbornik Mathematics, 1995
Summary: In 1928, \textit{G. H. Hardy} [Messenger Math. 58, 50-52 (1928; JFM 54.0310.03)] proved that the class \(L^p\) \((1\leq p< \infty)\) is invariant under the \((C, 1)\)-transformation of the Fourier coefficients. In 1944, \textit{R. Bellman} [Bull. Am. Math. Soc. 50, 741-744 (1944; Zbl 0060.18404)] proved the dual result for the class \(L^p\) \((
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The calculation of trigonometric fourier coefficients

Journal of Computational Physics, 1984
A method for the numerical evaluation of trigonometric Fourier coefficients \[ \frac{2}{B-A} \int^{B}_{A} f(x) {\cos\atop\sin} \left( \frac{2\pi r(x-A)}{B-A}\right) dx, \quad r=0,1,2,\ldots \] is described in terms of equally spaced function values \[ f(A+j(B-A)/m), \quad j=0,1,2,\ldots,m.
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ON CERTAIN INEQUALITIES FOR FOURIER COEFFICIENTS

SUT Journal of Mathematics, 1998
The paper contains an interesting historical survey of results on several fundamental inequalities including the Hausdorff-Young inequality for the Fourier transform and its sharpness, or the Carlson inequalities of both discrete and integral types.
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Fourier coefficients of and

The Mathematical Gazette, 2023
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