The sets of abstract trigonometric series induced by Lp

被引：0

作者：

Sikk J. ^{[1
]}

机构：

[1] Department of Mathematics, Estonian Agricultural University, Kreutzwaldi str. 5, Tartu

来源：

Results in Mathematics | 2000年 / 38卷 / 1-2期

关键词：

multipliers; summability; trigonometric series;

D O I：

10.1007/BF03322438

中图分类号：

学科分类号：

摘要：

The constructive character of Lp and the rate-summability provide starting-points for the present investigation. This paper considers the constructive spaces LTλ p and LTλ p. The constructive character of these spaces is determined by the rate λ. By appropriate λ’s the LTλ p forms the subspaces of Lp and the LTλ p forms the abstract sets of Fourier-Schwartz series. The constructive spaces preserve (in generalized form) the structural properties of Lp. It is used to develop the G. Goes method of complementary spaces and to consider the multipliers between different constructive spaces. © 2000, Birkhäuser Verlag, Basel.

引用

页码：152 / 165

页数：13

共 10 条

[1]

Butzer P.L., Scherer K., On the fundamental approximation theorems of D. Jackson, S. N. Berstein and theorems of M. Zamansky and S. B. Steĉkin, Aequationes math., 3, pp. 170-185, (1969)

[2]

Edwards R.E., Fourier Series. A modern introduction, (1967)

[3]

Goes G., BK-Räume und Matrixtransformationen für Fourierkoeffizienten, Math. Z., 70, pp. 345-371, (1959)

[4]

Goes G., Komplementräre Fourierkoeffizientenräume und Multiplikatoren, Math. Ann., 137, pp. 371-384, (1959)

[5]

Kangro G., Summability factors for the series λ-bounded by the methods of Riez and Cesàro, 277, pp. 136-154, (1971)

[6]

Kralik D., Elementary method of the theory of series in approximation theory, Math. Lapok., 28, pp. 27-33, (1980)

[7]

Sikk J., Complementary spaces with rapidity of Fourier coefficients, Tartu Ülik. Toimetised, 355, pp. 222-235, (1975)

[8]

Sikk J., Matrix mappings for rate-spaces and K-multipliers in the theory summability, Acta et Comm. Univ. Tartuensis, 846, pp. 118-128, (1989)

[9]

Sikk J., The rate-spaces m(λ), c(λ), c<sub>0</sub>(λ) and ℓ<sup>p</sup>(λ) of sequences, Acta et Comm. Univ. Tartuensis, 970, pp. 87-96, (1994)

[10]

Tonnov M., Summability factors, Fourier coefficients and multiplicators, Tartu Ülik. Toimetised, 192, pp. 82-97, (1966)

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