Skip to main content
Log in

Computation of the index of families of multidimensional operators in discrete-continual convolutions

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

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. R. Palais, Seminar on Atiyah-Singer Index Theorem, Princeton Univ. Press, Princeton (1965).

    Google Scholar 

  2. V. F. Atiyah, K-Theory, Benjamin, New York (1967).

    Google Scholar 

  3. W. Shih, “Fiber cobordism and the index of a family of elliptic differential operators,” Bull. Am. Math. Soc.,72, No. 6, 984–991 (1966).

    Google Scholar 

  4. A. S. Dynkin, “On the theory of pseudodifferential operators on a manifold with boundary,” Dokl. Akad. Nauk SSSR,186, No. 2, 251–253 (1969).

    Google Scholar 

  5. M. F. Atiyah and I. M. Singer, “The index of elliptic operators. IV,” Ann. Math.,93, 119–138 (1971).

    Google Scholar 

  6. M. F. Atiyah, “Algebraic topology and operators in Hilbert space,” Lectures in Modern Analysis and Applications. I, C. T. Taam (editor), Lecture Notes in Mathematics, Vol. 103, Springer-Verlag, Berlin-New York (1969), pp. 101–121.

    Google Scholar 

  7. M. A. Shubin, “On the index of a family of Wiener-Hopf operators,” Mat. Sb.,84, No. 4, 537–558 (1971).

    Google Scholar 

  8. I. B. Simonenko, “Convolution type operators in cones,” Mat. Sb.,74, No. 2, 298–313 (1967).

    Google Scholar 

  9. I. B. Simonenko, “On multidimensional discrete convolutions,” Mat. Issled., Shtiintsa, Kishinev,3, No. 1, 108–122 (1968).

    Google Scholar 

  10. V. M. Deundyak and V. S. Pilidi, “On a certain algebra of convolution type operators,” Mat. Issled., Shiintsa, Kishinev,9, No. 2, 28–37 (1974).

    Google Scholar 

  11. V. S. Pilidi, “On multidimensional bisingular operators,” Dokl. Akad. Nauk SSSR,201, No. 4, 787–789 (1971).

    Google Scholar 

  12. V. M. Deundyak, “On the computation of the index of systems of multidimensional bisingular integral operators,” Mat. Anal. Ego Prilozhen., Izd. Rostovsk. Gos. Univ., Rostov-on-Don, No. 7, 137–149 (1975).

    Google Scholar 

  13. M. F. Atiyah, “Algebraic topology and elliptic operators,” Commun. Pure Appl. Math.,20, 237–249 (1967).

    Google Scholar 

  14. E. H. Spanier, Algebraic Topology, McGraw-Hill, New York (1966).

    Google Scholar 

  15. V. N. Semenyuta and I. B. Simonenko, “On the index of generalized discrete convolutions,” Mat. Issled., Shtiintsa, Kishinev,4, No. 2, 88–94 (1969).

    Google Scholar 

  16. V. N. Semenyuta and I. B. Simonenko, “Computation of the index of generalized discrete convolutions,” Mat. Issled., Shtiintsa, Kishinev,4, No. 4, 134–141 (1969).

    Google Scholar 

  17. V. N. Semenyuta, “Computation of the index of generalized continual convolutions,” Mat. Issled., Shtiintsa, Kishinev,6, No. 2, 113–121 (1971).

    Google Scholar 

  18. R. G. Bartle and L. M. Graves, “Mappings between function spaces,” Trans. Am. Math. Soc.,72, No. 3, 400–413 (1952).

    Google Scholar 

Download references

Authors

Additional information

Agricultural-Machine Building Institute, Rostov-on-Don. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 20, No. 4, pp. 708–716, July–August, 1979.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Deundyak, V.M. Computation of the index of families of multidimensional operators in discrete-continual convolutions. Sib Math J 20, 492–498 (1979). https://doi.org/10.1007/BF00970362

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00970362

Navigation