Literature Cited
R. Palais, Seminar on Atiyah-Singer Index Theorem, Princeton Univ. Press, Princeton (1965).
V. F. Atiyah, K-Theory, Benjamin, New York (1967).
W. Shih, “Fiber cobordism and the index of a family of elliptic differential operators,” Bull. Am. Math. Soc.,72, No. 6, 984–991 (1966).
A. S. Dynkin, “On the theory of pseudodifferential operators on a manifold with boundary,” Dokl. Akad. Nauk SSSR,186, No. 2, 251–253 (1969).
M. F. Atiyah and I. M. Singer, “The index of elliptic operators. IV,” Ann. Math.,93, 119–138 (1971).
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.
M. A. Shubin, “On the index of a family of Wiener-Hopf operators,” Mat. Sb.,84, No. 4, 537–558 (1971).
I. B. Simonenko, “Convolution type operators in cones,” Mat. Sb.,74, No. 2, 298–313 (1967).
I. B. Simonenko, “On multidimensional discrete convolutions,” Mat. Issled., Shtiintsa, Kishinev,3, No. 1, 108–122 (1968).
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).
V. S. Pilidi, “On multidimensional bisingular operators,” Dokl. Akad. Nauk SSSR,201, No. 4, 787–789 (1971).
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).
M. F. Atiyah, “Algebraic topology and elliptic operators,” Commun. Pure Appl. Math.,20, 237–249 (1967).
E. H. Spanier, Algebraic Topology, McGraw-Hill, New York (1966).
V. N. Semenyuta and I. B. Simonenko, “On the index of generalized discrete convolutions,” Mat. Issled., Shtiintsa, Kishinev,4, No. 2, 88–94 (1969).
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).
V. N. Semenyuta, “Computation of the index of generalized continual convolutions,” Mat. Issled., Shtiintsa, Kishinev,6, No. 2, 113–121 (1971).
R. G. Bartle and L. M. Graves, “Mappings between function spaces,” Trans. Am. Math. Soc.,72, No. 3, 400–413 (1952).
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
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00970362