Results 281 to 290 of about 62,963 (321)
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Multipliers of double Fourier–Haar series
Advances in Operator Theory, 2021This paper is concerned with multiplier transformations for Fourier-Haar series. In the one-dimensional setting, the Fourier-Haar series of a function \(f\in L^1([0,1])\) is given by \[ f(x) \sim \sum_{n=1}^\infty a_n(f) \chi_n(x), \] where \(\{a_n(f)\}_{n\geq 1}\) is the Fourier-Haar coefficient of \(f\) and \(\{ \chi_n \}_{n\geq 1}\) is the Haar ...
N. T. Tleukhanova +2 more
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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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Fourier Multipliers for Besicovitch Spaces
Zeitschrift für Analysis und ihre Anwendungen, 1998In this paper a generalization of some results from Fourier analysis on periodic function spaces to the almost periodic case is given. We consider almost periodic distributions which constitute a subclass of tempered distributions. Under suitable conditions on the spectrum \Lambda \subset \
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Remarks on Walsh--Fourier multipliers
Publicationes Mathematicae Debrecen, 1998The author investigates special multiplier operators for one- and two-parameter Walsh-Paley systems. These multipliers were defined and partly investigated - with respect to their boundedness from \(H^p\) to \(L^p\) (for some \(p>0\)) - by the author [Acta Sci. Math. 64, No. 1-2, 183-200 (1998; preceding review) and Colloq. Math. 77, No. 1, 9-31 (1998;
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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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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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Multipliers of the fourier-haar series
Siberian Mathematical Journal, 2000The Haar system on \((0,1)\) is defined by the following equalities: \(\chi_0^0(t)=1\), \(\chi_n^k(t)=2^{n/2}\) for \(t\in ((k-1)2^{-n},(k-1/2)2^{-n})\), \(\chi_n^k(t)=-2^{n/2}\) for \(t\in ((k-1/2)2^{-n},k2^{-n})\), and \(\chi_n^k(t)=0\) for the remaining values of \(t\in (0,1)\), where \(1\leq k\leq 2^n\) and \(n=0,1,\dots\;\).
Bryskin, I. B. +2 more
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Operator Valued Fourier Multipliers
1999Results on Fourier multipliers are important tools in the study of partial differential equations. They represent a major step, for example, when establishing a priori estimates for solutions of parabolic evolution equations of Agmon-Douglis-Nirenberg type [1].
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