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I. B. Simonenko, “On multidimensional discrete convolutions,” Mat. Issled. Kishinev,3, No. 1, 108–122 (1968).
I. B. Simonenko, “A new general method of studying linear operator equations of the type of singular integral equations. I,” Izv. Akad. Nauk SSSR, No. 29, 567–586 (1965).
B. Ya. Shteinberg, “Operators of the type of discrete convolution, and the Noetherian property,” Mat. Zametki,23, No. 3, 417–423 (1978).
J. Favard, “Sur les équations différentielles à coefficients presque-périodiques,” Acta. Math.,51, 31–81 (1927).
É. M. Mukhamadiev, “On the invertibility of differential operators in partial derivatives of elliptic type,” Dokl. Akad. Nauk SSSR,205, No. 6, 1292–1295 (1972).
É. M. Mukhamadiev, “On the normal solubility and Noetherian property of elliptic operators in spaces of functions on Rn. I,” in: Boundary-Value Problems of Math. Physics and Combined Problems in the Theory of Functions [in Russian], Zap. Nauch. Sem. LOMI, Vol. 13 (1981), pp. 120–140.
I. Ts. Gokhberg and M. G. Krein, “Fundamental aspects of defects of numbers, root vectors and-indices of linear operators,” Usp. Mat. Nauk,12, No. 2, 44–118 (1957).
A. V. Kazak, “The local principle in the theory of projectional methods,” in: Integral and Differential Equations and Their Applications [in Russian], Izd. Kalm. Gos. Univ., Elista (1983), pp. 58–73.
M. A. Shubin, “Almost-periodic functions and differential operators,” Usp. Mat. Nauk,33, No. 2, 3–47 (1978).
A. V. Kazak and I. V. Simonenko, “Projectional methods for solving multidimensional discrete equations in convolutions,” Sib. Mat. Zh.,21, No. 2, 119–127 (1980).
A. V. Lebedev, “The invertibility of elements in algebras with a shift. I,” Izv. Akad. Nauk BSSR, No. 3, 41–47 (1983).
B. V. Lange and V. S. Rabinovich, “The algebra of operators of a generalized discrete convolution with oscillating coefficients,” Dep. VINITI No. 3661–82.
A. Bettkher and A. É. Pasenchuk, “On the invertibility of Wiener-Hopf operators in a quarter-plane, with kernels whose supports are situated in a half plane,” in: Differential and Integral Equations and Their Applications [in Russian], Izd. Kalm. Gos. Univ., Elista (1982), pp. 9–18.
Translated from Matematicheskie Zametki, Vol. 37, No. 3, pp. 407–421, March, 1985.
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Lange, B.V., Rabinovich, V.S. Noether property for multidimensional discrete Convolution operators. Mathematical Notes of the Academy of Sciences of the USSR 37, 228–237 (1985). https://doi.org/10.1007/BF01158746
- Convolution Operator
- Discrete Convolution
- Discrete Convolution Operator