Results 261 to 270 of about 3,568,332 (307)

On the Asymptotic Distribution of Fourier Coefficients of Cusp Forms

Bulletin of the Brazilian Mathematical Society, New Series, 2023
Huafeng Liu
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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 THE MAGNITUDE OF FOURIER COEFFICIENTS II

Analysis, 2004
The problem indicated in the title is studied for functions defined on \(T^2\), where \(T := [-\pi,\pi]\), and which belong to various classes of functions of generalized bounded variation. Three theorems are proved. In Theorem 1 estimates are proved for functions in \(\text{BV}_V (T^2)\) (Vitali) and BV\(_{HK}\) (Hardy and Krause); in Theorem 2 for ...
Schramm, Michael, Waterman, Daniel
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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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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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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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On the coefficient quantization of the fourier basis

IEEE Transactions on Signal Processing, 2003
A family of function bases is devised from a superposition of unit characteristic functions. It is shown that these simple bases can be used to perform a quantized Fourier transform. Furthermore, the transform can be implemented in an iterative scheme such that system resources are balanced in accordance with performance.
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General Fourier coefficients

Acta Mathematica Hungarica, 2019
L. Gogoladze, V. Tsagareishvili
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Improved Fourier Coefficients for Maps Using Phases from Partial Structures with Errors

, 1986
Randy J. Read
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