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Literature Cited
B. Ya. Shteinberg, “On convolution-type operators on locally compact groups,” Funkts. Anal. Prilozhen.,15, No. 3, 95–96 (1981).
B. Ya. Shteinberg, “Convolution-type operators on locally compact groups,” Rostov on Don (1980), Dep. at VINITI, 26.02.80, No. 715-80.
I. B. Simonenko, “A new general method for investigation of linear operator equations of the type of singular integral equations. 1,” Izv. Akad. Nauk SSSR. Ser. Mat.,29, No. 3, 567–586 (1965).
I. B. Simonenko and Chin' Ngok Min', A Local method in the Theory of One-dimensional Singular Integral Equations with Piecewise Continuous Coefficients. Noethericity [in Russian], Izd. Rostov. Gos. Univ., Rostov on Don (1986).
B. Ya. Shteinberg, “On the index of convolution operators with slowly varying coefficients inL p (Rk×Zl),” in: Differential, Integral Equations and Complex Analysis [in Russian], Izd. Kalmytsk. Gos. Univ., Elista (1986), pp. 153–163.
V. M. Deundyak and B. Ya. Shteinberg, “On the index of convolution operators with slowly varying coefficients on abelian groups,” Funkts. Anal. Prilozhen.,19, No. 4, 84–85 (1985).
M. Atiyah, Lectures on K-Theory [Russian translation], Mir, Moscow (1967).
J. Eells, “Freedholm structures,” Proc. Symp. Pure Math.,18, No. 1, 62–85 (1970).
M. A. Shubin, “On the index of families of Wiener-Hopf operators,” Mat. Sb.,84, No. 4, 537–558 (1971).
V. M. Deundyak, “On the tensor product of algebras of discrete-continual convolutions,” Izv. Severo-Kavkaz. Nauchn. Tsentra Vyssh. Shkoly. Estestv. Nauki, No. 4, 59–61 (1977).
M. Atiyah, “Algebraic topology and operators in Hilbert space,” Lecture Notes Math., Springer, Berlin,103, (1969), pp. 101–102.
V. M. Deundyak, “Computation of the index of families of many dimensional operators in discrete-continual convolutions,” Sib. Mat. Zh.,20, No. 4, 708–716 (1979).
I. B. Simonenko, “Convolution-type operators in cones,” Mat. Sb.,74, No. 2, 298–313 (1967).
N. Bourbaki, Eléments de Mathématique. Théories Spectrales [Russian translation], Mir, Moscow (1972).
M. Karoubi, K-Theory. An Introduction [Russian translation], Mir, Moscow (1981).
E. H. Spanier, Algebraic Topology, McGraw-Hill, New York (1966).
E. Michael, “Convex structures and continuous selections,” Canad. J. Math.,11, No. 4, 556–575 (1959).
M. Karobui, “K-théorie algébrique de certains algébres d'opérateurs,” Lecture Notes Math., Springer, Berlin,725, (1979), pp. 254–290.
I. B. Simonenko, “On many-dimensional discrete convolutions,” in: Matematicheskie Issledovaniya, Shtiintsa, Kishinev,3, No. 1 (1968), pp. 108–122.
V. M. Deundyak and V. S. Pildi, “On an algebra of convolution-type operators,” in: Matematicheskie Issledovaniya, Shtiintsa, Kishinev,3, No. 1 (1974), pp. 28–39.
V. N. Semenyuta and I. B. Simonenko, “Computation of the index of generalized discrete convolutions,” in: Matematicheskie Issledovaniya, Shtiintsa, Kishinev,4, No. 4 (1969), pp. 131–141.
V. N. Semenyuta, “Computation of the index of generalized continual convolutions,” in: Matematicheskie Issledovaniya, Shtiintsa, Kishinev,6, No. 2 (1971), pp. 113–121.
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Rostov on Don. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 1, pp. 70–78, January–February, 1990.
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Deundyak, V.M. Index of families of convolution operators on Abelian groups. Sib Math J 31, 58–66 (1990). https://doi.org/10.1007/BF00971150
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DOI: https://doi.org/10.1007/BF00971150