Skip to main content
Log in

Conditions under which certain systems of analytic functions related to a generalized differentiation operator form a quasipower basis

  • Brief Communications
  • Published:
Ukrainian Mathematical Journal Aims and scope

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.

Literature cited

  1. N. I. Nagnibida, Continuous Linear Operators in Analytic Spaces Which Commute with the Differentiation Operator [in Russian], Theory of Functions, Functional Analysis, and Their Applications, Vol. 2, Izd. Kh. G. U. (1966).

  2. M. G. Khaplanov, “A matrix test for a basis in a space of analytic functions,” Dokl. Akad. Nauk SSSR,80, No. 2 (1951).

  3. A. I. Markushevich, “A basis in a space of analytic functions,” Matem. Sb.,17(59), No. 2 (1945).

  4. M. G. Khaplanov, Completeness of Certain Systems of Analytic Functions [in Russian], Uch. Zap. Rostovsk. na Don Ped. In-ta., Vol. 3 (1955).

  5. K. M. Fishman and G. M. Sas'ko, “On certain systems of functions which form quasipower bases in spaces of functions analytic in a disk,” Dokl. Akad. Nauk SSSR,146, No. 2 (1962).

  6. V. I. Gorgula and N. I. Nagnibida, “Conditions under which a system of analytic functions form a basis,” Ukrainsk. Matem. Zh.,24, No. 6 (1972).

  7. N. I. Nagnibida, “A basis of a space of functions analytic in a disk,” Sibirsk. Matem. Zh.,11, No. 2 (1970).

  8. Yu. A. Kaz'min, “Infinite systems of linear equations and bases of analytic functions,” Dokl. Akad. Nauk SSSR,106, No. 2 (1956).

  9. I. I. Ibragimov, Methods of Interpolation of Functions and Some Applications [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  10. M. G. Khaplanov, “Linear mappings of analytic spaces,” Dokl. Akad. Nauk SSR,80, No. 1 (1951).

  11. K. M. Fishman, “Linear mappings of analytic spaces,” Dokl. Akad. Nauk SSSR,127, No. 1 (1959).

  12. S. M. Nikol'skii, “Linear equations in normed linear spaces,” Izv. Akad. Nauk SSSR, Ser, Matem.,7, No. 3 (1943).

  13. K. M. Fishman and N. I. Nagnibida, “A basis of generalized antiderivatives,” Sibirsk. Matem. Zh.,6, No. 4 (1965).

  14. S. Banach, A Course in Functional Analysis [in Polish], Radyans'ka Shkola, Krakow (1948).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 27, No. 1, pp. 110–117, January–February, 1975.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Linchuk, S.S., Nagnibida, N.I. Conditions under which certain systems of analytic functions related to a generalized differentiation operator form a quasipower basis. Ukr Math J 27, 90–95 (1975). https://doi.org/10.1007/BF01085849

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01085849

Keywords

Navigation