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Necessary and sufficient conditions for an orthogonal series to be the Fourier series of a function in the space
,
, are obtained. In the special case of regular summation methods we recover the classical results of Orlicz and Lomnicki. 相似文献
2.
I. N. Brui 《Mathematical Notes》1997,62(5):566-574
Suppose that a lower triangular matrix μ:[μ
m
(n)
] defines a conservative summation method for series, i.e.,
and the sequence (ρ
m
,m ∈ ℤ0), is bounded away from zero. Then the trigonometric series
is the Fourier series of a functionf ∈L
p
(
), wherep ε ]1; ∞[, if and only if the sequence ofp-norms of its μ-means is bounded:
In the case of the Fejér method, we have the test due to W. and G. Young (1913). In the case of the Fourier method, we obtain
the converse of the Riesz theorem (1927).
Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 677–686, November, 1997.
Translated by N. K. Kulman 相似文献
3.
E. A. Brui A. V. Shchelokova A. V. Sokolov A. P. Slobozhanyuk A. E. Andreychenko V. A. Fokin P. A. Belov I. V. Melchakova 《JETP Letters》2018,108(6):423-427
A hybrid metasurface realized by a double array of brass wires inserted into two high-permittivity dielectric slabs at both sides was used to perform a magnetic resonance spectroscopy experiment at a 1.5 T clinical magnetic resonance scanner. The metasurface coupled inductively to a transceive birdcage body coil located within the scanner’s bore. The metasurface demonstrated an enhancement of the signal-to-noise ratio of the magnetic resonance spectroscopy experiment in vitro. Up to a signal-to-noise ratio gain of 7.4 for choline and creatine spectral lines was observed in the presence of the metasurface compared to the body coil alone. 相似文献
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