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Ukrainian Mathematical Journal, 1991
Let \(S\) be a nonempty set of integers, and let \(C_ S(T)\) be a subspace of those \(f\) of \(C(T)\), \(T=(-\pi,\pi]\) whose spectrum is in \(S\), i.e., \(\{k:\hat f(k)\neq 0\}\subset S\). The paper deals with new propositions for multipliers of trigonometrical Fourier series in the spaces \(C(T)\) and \(C_ S(T)\).
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Let \(S\) be a nonempty set of integers, and let \(C_ S(T)\) be a subspace of those \(f\) of \(C(T)\), \(T=(-\pi,\pi]\) whose spectrum is in \(S\), i.e., \(\{k:\hat f(k)\neq 0\}\subset S\). The paper deals with new propositions for multipliers of trigonometrical Fourier series in the spaces \(C(T)\) and \(C_ S(T)\).
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On multipliers of Fourier transforms
Mathematical Proceedings of the Cambridge Philosophical Society, 1972In this paper G is a locally compact Abelian group, φ a complex-valued function defined on the dual Γ, Lp(G) (1 ≤ p ≤ ∞) the usual Lebesgue space of index p formed with respect to Haar measure, C(G) the set of all bounded continuous complex-valued functions on G, and C0(G) the set of all f ∈ C(G) which vanish at infinity.
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Multipliers of Fourier Transforms
2002In this chapter weighted Triebel-Lizorkin spaces are defined in a general settiing. The two-weighted criteria for fractional and singular integrals derived in the previous chapters enable us to develop a new approach to the theory of multipliers of Fourier transforms.
David E. Edmunds +2 more
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Construction of Fourier multipliers
Bulletin of the Australian Mathematical Society, 1977The classical Wiener-Pitt phenomenon for measures may be formulated as an existence theorem for Fourier multipliers with irregular, spectral properties and the result has been refined in various ways over the years. The most recent development is due to Zafran, who exhibits abnormal spectral behaviour in multipliers whose transforms vanish at infinity ...
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1997
In this section we investigate multipliers with respect to the H.s. A sequence λ n , k , (n, k) ∈ Ω generates the operator $$ \Lambda (\sum\limits_{(n,k) \in \Omega } {{a_{n,k}}x_n^k} ) = \sum {{\lambda _{n,k}}{c_{n,k}}x_n^k} $$ (1) on the polynomials with respect to the H.s. Such operators are said to be multipliers.
Igor Novikov, Evgenij Semenov
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In this section we investigate multipliers with respect to the H.s. A sequence λ n , k , (n, k) ∈ Ω generates the operator $$ \Lambda (\sum\limits_{(n,k) \in \Omega } {{a_{n,k}}x_n^k} ) = \sum {{\lambda _{n,k}}{c_{n,k}}x_n^k} $$ (1) on the polynomials with respect to the H.s. Such operators are said to be multipliers.
Igor Novikov, Evgenij Semenov
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On Compactness of Commutators of Multiplications and Fourier Multipliers
Mediterranean Journal of Mathematics, 2018We generalise results on compactness of commutators of multiplications and Fourier multiplier operators by Cordes (J Funct Anal 18:115–131, 1975) with respect to the smoothness of multiplication function. Our prime motivation has been a particular case known as the first commutation lemma—the basic tool for defining H-measures and H-distributions.
Nenad Antonić +2 more
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On multipliers of double Fourier series
1986Translation from Uch. Zap. Tartu. Gos. Univ. 504(1979), 116-125 (1981; Zbl 0521.42018).
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