Skip to main content
SpringerLink
Log in

Scalar discrete convolutions in spaces of sequences summed with exponential weights. Part 2: one-sided and generalized invertibility

  • Original Article
  • Published:
Boletín de la Sociedad Matemática Mexicana Aims and scope Submit manuscript

Abstract

A theory of the invertibility of discrete composite convolution operators in the space of sequences summed with exponential weight is constructed. In this part we consider those situations when generalized invertible operators exist along with one-sided invertible \(\varPhi \)-operators. The constructions of the one-sided and generalized inverse operators are given.

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

References

  1. Boichuk, A.A., Zhuravlev, V.F., Samoilenko, A.M.: Generalized inverse operators and noether boundary-value problems. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1995) (Russian)

  2. Dybin V.B., Dzhirgalova S.B.: The operator of discrete convolution in space \(\{\alpha ,\beta \}_p\), \(1\le p\le \infty \). Scientific-educational and applied journal university news, Northern-caucasus region. Natural Sciences Series 9, Appendix, 3–16 (2003)

  3. Dybin V.B., Dzhirgalova S.B.: Compound discrete convolutions in space \(\{\alpha ,\beta \}_p, 1\le p\le \infty \). Part I. Rostov State University, Collection of preprints VINITI, 14.01.03. No. 90 (2003)

  4. Dybin, V.B., Dzhirgalova, S.B.: Scalar compound discrete convolutions in space \(\{\alpha ,\beta \}_p\), \(1\le p\le \infty \). One-sided convertibility. Scientic-educational and applied journal university news, North-caucasian region, Natural sciences series. Special issue: Pseudo-differential equations and some problems of mathematical physics, 56–63 (2005)

  5. Dybin, V.B., Dzhirgalova, S.B.: Scalar discrete convolutions in spaces of sequences summed with exponential weights. Part 1: One-sided invertibility. Integr. Equ. Oper. Theory 82, 575–600 (2015). doi:10.1007/s00020-014-2207-0

    Article  MathSciNet  MATH  Google Scholar 

  6. Gelfand, I.M., Raikov, D.A., Shilov, G.E.: Commutative normed rings. Chelsea, New York (1964)

  7. Gohberg, I., Krupnik, N.Y.: One-dimensional linear singular integral equations, vol. I. Birkhäuser Verlag, Basel, Boston, Berlin (1992)

  8. Gohberg I., Feldman I.A.: Convolution equations and projection methods for their solution. AMS, Providence (1974)

  9. Gohberg, I., Krein, M.G.: On a dual integral equation and its transpose I. Teoret. Prikl. Mat. Vyp. 1, 58–81 (1958) (Russian) (1958)

  10. Kurosh, A.G.: Lectures on general algebra. Chelsea Publishing Company, New York (1963)

  11. Pasenchuk, A.E.: Abstract singular operators. Novocherkassk Polytechnic University Press, Novocherkassk (1993) (Russian)

  12. Zygmund, A.: Trigonometric series, vol. II, 2nd ed. Cambridge University Press, Cambridge (1959)

Download references

Author information

Authors and Affiliations

  1. Chair of Algebra and Discrete Mathematics, Southern Federal University, 105/42, Bolshaya Sadovaya Str., Rostov-on-Don, 344006, Russia

    V. B. Dybin

  2. Chair of Algebra and Analysis Faculty of Mathematics, Physics and Information Technologies, Kalmyk State University, 11, Pushkin Street, Elista, 358000, Kalmyk Republic, Russia

    S. B. Dzhirgalova

Authors
  1. V. B. Dybin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. B. Dzhirgalova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. B. Dybin.

Additional information

To Professor Sergei Mikhailovich Grudsky on the occasion of his 60th birthday.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dybin, V.B., Dzhirgalova, S.B. Scalar discrete convolutions in spaces of sequences summed with exponential weights. Part 2: one-sided and generalized invertibility. Bol. Soc. Mat. Mex. 22, 337–360 (2016). https://doi.org/10.1007/s40590-016-0102-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40590-016-0102-1

Keywords

Mathematics Subject Classification

Search

Navigation