Results 271 to 280 of about 79,804 (306)
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ON THE MAGNITUDE OF FOURIER COEFFICIENTS II
Analysis, 2004The 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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Instability Phenomena for the Fourier Coefficients
Mathematische Nachrichten, 1996AbstractLet 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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Asymptotic Estimates of Fourier Coefficients
SIAM Journal on Mathematical Analysis, 1974Complex 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, 1995Summary: 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 the coefficient quantization of the fourier basis
IEEE Transactions on Signal Processing, 2003A 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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ON CERTAIN INEQUALITIES FOR FOURIER COEFFICIENTS
SUT Journal of Mathematics, 1998The 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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Differentiable functions and their Fourier coefficients
Georgian Mathematical Journal, 2021Vakhtang Tsagareishvili
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Signs of Fourier coefficients of cusp form at sum of two squares
Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2020Manish Kumar Pandey
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