Skip to main content
Log in

On the structure of the class A(ϕ)

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

In this paper, we study whether the set A(ϕ) is closed under multiplication f · g, where f and g belong to the class A(ϕ). We also study the problem of the existence of a solution of the equation Bx = C (where B,CA(ϕ) and B ≠ 0) on the set A(ϕ).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Bibliography

  1. J.-P. Kahane, Séries de Fourier absolument convergentes, Springer-Verlag, Berlin-New York, 1970; Russian transl.: Moscow, Mir, 1976

    MATH  Google Scholar 

  2. P. L. Ul’yanov, “On the absolute convergence of trigonometric Fourier series,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 322 (1992), no. 2, 253–258.

    MathSciNet  Google Scholar 

  3. V. Bugadze, Fourier-Haar Series of the Superposition of Functions [in Russian], Tbilisi, 1988.

  4. S. V. Bochkarev, “Absolute convergence of Fourier series with respect to general orthogonal complete systems,” Uspekhi Mat. Nauk [Russian Math. Surveys], 27 (1972), no. 1, 53–76.

    Google Scholar 

  5. V. Tsagareishvili, Classes of Functions and Fourier Coefficients [in Russian], Doctoral (Phys.-Math.) Dissertation, Tbilisi, 2004.

  6. P. L. Ul’yanov, “On series in the Haar system,” Mat. Sb. [Math. USSR-Sb.], 63(105) (1964), no. 3, 356–391.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Matematicheskie Zametki, vol. 80, no. 2, 2006, pp. 296–308.

Original Russian Text Copyright © 2006 by V. Tsagareishvili.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tsagareishvili, V. On the structure of the class A(ϕ). Math Notes 80, 284–295 (2006). https://doi.org/10.1007/s11006-006-0137-0

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11006-006-0137-0

Key words

Navigation