Advertisement

Ukrainian Mathematical Journal

, Volume 27, Issue 1, pp 90–95 | Cite as

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

  • S. S. Linchuk
  • N. I. Nagnibida
Brief Communications

Keywords

Analytic Function Generalize Differentiation Differentiation Operator Generalize Differentiation Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 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).Google Scholar
  2. 2.
    M. G. Khaplanov, “A matrix test for a basis in a space of analytic functions,” Dokl. Akad. Nauk SSSR,80, No. 2 (1951).Google Scholar
  3. 3.
    A. I. Markushevich, “A basis in a space of analytic functions,” Matem. Sb.,17(59), No. 2 (1945).Google Scholar
  4. 4.
    M. G. Khaplanov, Completeness of Certain Systems of Analytic Functions [in Russian], Uch. Zap. Rostovsk. na Don Ped. In-ta., Vol. 3 (1955).Google Scholar
  5. 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).Google Scholar
  6. 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).Google Scholar
  7. 7.
    N. I. Nagnibida, “A basis of a space of functions analytic in a disk,” Sibirsk. Matem. Zh.,11, No. 2 (1970).Google Scholar
  8. 8.
    Yu. A. Kaz'min, “Infinite systems of linear equations and bases of analytic functions,” Dokl. Akad. Nauk SSSR,106, No. 2 (1956).Google Scholar
  9. 9.
    I. I. Ibragimov, Methods of Interpolation of Functions and Some Applications [in Russian], Nauka, Moscow (1971).Google Scholar
  10. 10.
    M. G. Khaplanov, “Linear mappings of analytic spaces,” Dokl. Akad. Nauk SSR,80, No. 1 (1951).Google Scholar
  11. 11.
    K. M. Fishman, “Linear mappings of analytic spaces,” Dokl. Akad. Nauk SSSR,127, No. 1 (1959).Google Scholar
  12. 12.
    S. M. Nikol'skii, “Linear equations in normed linear spaces,” Izv. Akad. Nauk SSSR, Ser, Matem.,7, No. 3 (1943).Google Scholar
  13. 13.
    K. M. Fishman and N. I. Nagnibida, “A basis of generalized antiderivatives,” Sibirsk. Matem. Zh.,6, No. 4 (1965).Google Scholar
  14. 14.
    S. Banach, A Course in Functional Analysis [in Polish], Radyans'ka Shkola, Krakow (1948).Google Scholar

Copyright information

© Plenum Publishing Corporation 1975

Authors and Affiliations

  • S. S. Linchuk
    • 1
  • N. I. Nagnibida
    • 1
  1. 1.Chernovtsy State UniversityUSSR

Personalised recommendations