The Fourier transforms of Lipschitz functions on certain domains.
Younis, M.S. (1997)
International Journal of Mathematics and Mathematical Sciences
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Younis, M.S. (1997)
International Journal of Mathematics and Mathematical Sciences
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Younis, M.S. (1986)
International Journal of Mathematics and Mathematical Sciences
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Younis, M.S. (2001)
International Journal of Mathematics and Mathematical Sciences
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Younis, M.S. (1998)
International Journal of Mathematics and Mathematical Sciences
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Ferenc Móricz (2010)
Studia Mathematica
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We consider complex-valued functions f ∈ L¹(ℝ), and prove sufficient conditions in terms of f to ensure that the Fourier transform f̂ belongs to one of the Lipschitz classes Lip(α) and lip(α) for some 0 < α ≤ 1, or to one of the Zygmund classes zyg(α) and zyg(α) for some 0 < α ≤ 2. These sufficient conditions are best possible in the sense that they are also necessary in the case of real-valued functions f for which either xf(x) ≥ 0 or f(x) ≥ 0 almost everywhere.
Younis, M.S. (2000)
International Journal of Mathematics and Mathematical Sciences
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Tong-Seng Quek, Leonard Y.H. Yap (1983)
Mathematische Zeitschrift
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Walter R. Bloom (1982)
Colloquium Mathematicae
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Raimond Struble (1984)
Studia Mathematica
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M. Bożejko, T. Pytlik (1972)
Colloquium Mathematicae
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Ferenc Móricz (2008)
Colloquium Mathematicae
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We investigate the order of magnitude of the modulus of continuity of a function f with absolutely convergent Fourier series. We give sufficient conditions in terms of the Fourier coefficients in order that f belong to one of the generalized Lipschitz classes Lip(α,L) and Lip(α,1/L), where 0 ≤ α ≤ 1 and L = L(x) is a positive, nondecreasing, slowly varying function such that L(x) → ∞ as x → ∞. For example, a 2π-periodic function f is said to belong to the class Lip(α,L) if for all...
Zhang, Qing-Hua, Chen, Shuiming, Qu, Yuanyuan (2005)
International Journal of Mathematics and Mathematical Sciences
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Leonede De Michele, Marina Di Natale, Delfina Roux (1990)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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In this paper a very general method is given in order to reconstruct a periodic function knowing only an approximation of its Fourier coefficients.