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Multipliers of the fourier-haar series

Siberian Mathematical Journal, 2000
The 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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Remarks on Walsh--Fourier multipliers

Publicationes Mathematicae Debrecen, 1998
The 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 double Fourier–Haar series

Advances in Operator Theory, 2021
This 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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Fourier Multipliers for Besicovitch Spaces

Zeitschrift für Analysis und ihre Anwendungen, 1998
In 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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The multiplier based on quantum Fourier transform

CCF Transactions on High Performance Computing, 2020
In the paper, we first present a quantum multiplier based on quantum Fourier transform (QFT), which is composed by a series of double-controlled phase gates, the control qubits are from the two multipliers, and the controlled qubits are in the ancillary state.
Anqi Zhang, Xuemei Wang, Shengmei Zhao
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