Skip to main content
SpringerLink
Log in

A right inverse operator of the convolution operator

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

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

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature cited

  1. L. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces [in Russian], Fizmatgiz, Moscow (1959).

    Google Scholar 

  2. R. Edwards, Functional Analysis [Russian translation], Mir, Moscow (1969).

    Google Scholar 

  3. S. N. Melikhov, “Absolutely converging series in canonical inductive limits,” Mat. Zametki,39, No. 6, 877–886 (1986).

    Google Scholar 

  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. H. Muggly, “Differentialgleichungen unendlich hoher Ordnung mit konstanten Koeffizienten,” Comment. Math. Helv., No. 1, 151–179 (1938).

    Google Scholar 

  6. B. Ya. Levin, Distribution of Roots of Entire Functions [in Russian], Gostekhteoretizdat, Moscow (1956).

    Google Scholar 

  7. A. F. Leont'ev, Entire Functions. Exponent Series [in Russian], Nauka, Moscow (1983).

    Google Scholar 

  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. 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. 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. 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. Yu. F. Korobeinik, “Shift operators in number families,” Rostov on Don, Izd. Rostov Inst. (1983).

  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. 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. 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. 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 

Download references

Author information

Authors and Affiliations

  1. Rostov University, USSR

    Yu. F. Korobeinik

Authors
  1. Yu. F. Korobeinik
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 9, pp. 1167–1176, September, 1991.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Korobeinik, Y.F. A right inverse operator of the convolution operator. Ukr Math J 43, 1094–1101 (1991). https://doi.org/10.1007/BF01089208

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01089208

Keywords

Search

Navigation