Subsystems of the Haar system in spacesE
ϕ with
$$\mathop {lim}\limits_{\overline {t \to \infty } } \frac{{\varphi  (t)}}{t} = 0$$

V. I. Filippov

doi:10.1007/bf01263305

journal article Jun 01, 1992

Subsystems of the Haar system in spacesE ϕ with $$\mathop {lim}\limits_{\overline {t \to \infty } } \frac{{\varphi (t)}}{t} = 0$$

V. I. Filippov

Mathematical Notes Vol. 51 No. 6 pp. 593-599 · Springer Science and Business Media LLC

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References

9

[1]

P. L. Ul'yanov, “Series representations of functions and the classes ϕ(L) ” Usp. Mat. Nauk,27, 3–52 (1972).

[2]

J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math. 1034, Springer (1983). 10.1007/bfb0072210

[3]

V. I. Ivanov, “Representation of measurable functions by multiple trigonometric series,” Dokl. Akad. Nauk SSSR,259, No. 2, 279–282 (1981).

[4]

P. Oswald, “On some convergence properties of Haar —Fourier series in the classesϕ(L)” Acta Math. Hung.,42, Nos. 3–4, 279–293 (1983). 10.1007/bf01956776

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V. I. Ivanov, “Representation of functions in metric symmetrical spaces without linear functionals,” Dokl. Akad. Nauk SSSR,289, No. 3, 532–535 (1986).

[6]

V. I. Filippov, “Criterion for the existence of linear continuous nonzero functionals and nonuniqueness of representations in spacesE ϕ” Teor. Funkts. Priblizhen. Trudy 3 Saratov. Zimnei Shkoly 1986,3, 74–76 (1988).

[7]

A. A. Talalyan, “On approximation properties of certain incomplete systems,” Mat. Sb.,115, No. 4, 499–541 (1981).

[8]

V. I. Filippov, “On subsystems of the Faber-Schauder system in spacesE ϕ” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 2, 78–95 (1991).

[9]

J. Price and R. E. Zink, “On sets of completeness for families of Haar functions,” Trans. Am. Math. Soc.,119, No. 2, 262–269 (1965). 10.1090/s0002-9947-1965-0184023-x

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Published: Jun 01, 1992
Vol/Issue: 51(6)
Pages: 593-599
License: View

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V. I. Filippov

Cite This Article

V. I. Filippov (1992). Subsystems of the Haar system in spacesE ϕ with $$\mathop {lim}\limits_{\overline {t \to \infty } } \frac{{\varphi (t)}}{t} = 0$$. Mathematical Notes, 51(6), 593-599. https://doi.org/10.1007/bf01263305

Subsystems of the Haar system in spacesE ϕ with $$\mathop {lim}\limits_{\overline {t \to \infty } } \frac{{\varphi (t)}}{t} = 0$$

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