Abstract
Theorems on the inversion of Toeplitz matrices ∥a j-k ∥ n j, k=0 consisting of complex numbers are obtained in [1], [2]. In this paper those results are generalized to the case where a j (j = 0,±1,...,±n) are elements of some noncommutative algebra with unit. The paper consists of six sections. The results of [1] are generalized in the first three sections, the results of [2] are extended in the last three sections. Continual analogues of results of this paper will be presented elsewhere.
The paper was originally published as ИЦ. Гохберг, Г. ХаЙниг, Обращешие конеЧных тэпницовых матриц, составлонных из эломонтов нскоммутативной алгсбры, Rev. Roumaine Math. Pures Appl. 19 (1974), 623–663. MR0353040 (50 #5526), Zbl 0337.15005.
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References
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Gohberg, I., Heinig, G. (2010). Inversion of Finite ToeplitzMatrices Consisting of Elements of a Noncommutative Algebra. In: Lerer, L., Olshevsky, V., Spitkovsky, I.M. (eds) Convolution Equations and Singular Integral Operators. Operator Theory: Advances and Applications, vol 206. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8956-7_3
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