Ukrainian Mathematical Journal

, Volume 43, Issue 9, pp 1094–1101 | Cite as

A right inverse operator of the convolution operator

  • Yu. F. Korobeinik


We give a description of a linear continuous right inverse operator of a convolution operator in spaces of analytic functions with an exponential basis.


Analytic Function Inverse Operator Convolution Operator Exponential Basis 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    L. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces [in Russian], Fizmatgiz, Moscow (1959).Google Scholar
  2. 2.
    R. Edwards, Functional Analysis [Russian translation], Mir, Moscow (1969).Google Scholar
  3. 3.
    S. N. Melikhov, “Absolutely converging series in canonical inductive limits,” Mat. Zametki,39, No. 6, 877–886 (1986).Google Scholar
  4. 4.
    Yu. F. Korobeinik, “A dual problem. 1. General results. Applications to Frechet spaces,” Mat. Sb.,97, No. 2, 193–229 (1975).Google Scholar
  5. 5.
    H. Muggly, “Differentialgleichungen unendlich hoher Ordnung mit konstanten Koeffizienten,” Comment. Math. Helv., No. 1, 151–179 (1938).Google Scholar
  6. 6.
    B. Ya. Levin, Distribution of Roots of Entire Functions [in Russian], Gostekhteoretizdat, Moscow (1956).Google Scholar
  7. 7.
    A. F. Leont'ev, Entire Functions. Exponent Series [in Russian], Nauka, Moscow (1983).Google Scholar
  8. 8.
    S. Momm, “Partial differential operators of infinite order with constant coefficients on the space of analytic functions on the polydisc,” Stud. Math.,46, 51–71 (1990).Google Scholar
  9. 9.
    A. O. Gel'fond, “Linear differential equations with constant coefficients of infinite order and asymptotic periods of entire functions,” Tr. Mat. Inst.,38, 42–67 (1951).Google Scholar
  10. 10.
    R. Meise and B. A. Taylor, “Each nonzero convolution operator on the entire functions admits a continuous linear right inverse,” Math. Zh.,197, 139–152 (1988).Google Scholar
  11. 11.
    P. Sikkema, “Differential operators and differential equations of finite order with constant coefficients,” in: Researches in Connection with Integral Functions of Finite Order,” Noordhoff, Groningen (1953).Google Scholar
  12. 12.
    Yu. F. Korobeinik, “Shift operators in number families,” Rostov on Don, Izd. Rostov Inst. (1983).Google Scholar
  13. 13.
    R. Meise and B. A. Taylor, “Splitting of closed ideals in (DFN)-algebras of entire functions and the property (DN),” Trans. Am. Math. Soc.,302, 341–370 (1987).Google Scholar
  14. 14.
    R. Meise and B. A. Taylor, “Sequence space representation for (FN)-algebras of entire functions modulo closed ideals,” Stud. Math.,125, 203–227 (1987).Google Scholar
  15. 15.
    A. Hurwitz, “Sur l'integrale finie d'une fonction entiere,” Acta. Math.,20, 285–312 (1897); Gesammelte Abhandlungen. Bd. 1, 436–459.Google Scholar
  16. 16.
    M. N. Sheremeta, “Relation between the growth of the maximum of the modulus of an entire function and the modulus of the coefficients of its power expansion,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 2, 100–108 (1967).Google Scholar

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • Yu. F. Korobeinik
    • 1
  1. 1.Rostov UniversityUSSR

Personalised recommendations