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Scalar Discrete Convolutions in Spaces of Sequences Summed with Exponential Weights—Part 1: One-Sided Invertibility

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Abstract

The theory of the one-sided invertibility of discrete composite convolution operators in the space of sequences summed with exponential weight is constructed. In this part we consider those situations when Φ-theory of the operators is the same as the theory of their one-sided invertibility. The kernels and co-kernels of the operators are described. Constructions of the one-sided inverse operators are given.

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Authors and Affiliations

  1. Chair Algebra and Discrete Mathematics, Southern Federal University, 105/42, Bolshaya Sadovaya Str., Rostov-on-Don, 344006, Russia

    V. B. Dybin

  2. Chair Algebra and Analysis Faculty of Mathematics, Physics and Information Technologies, Kalmyk State University, 11, Pushkin Street, Elista, 358000, Kalmyk Republic, Russia

    S. B. Dzhirgalova

Authors
  1. V. B. Dybin
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  2. S. B. Dzhirgalova
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Correspondence to V. B. Dybin.

Additional information

V. B. Dybin: This work was completed with the support of Southern Federal University, internal grant 05/6-89.

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Dybin, V.B., Dzhirgalova, S.B. Scalar Discrete Convolutions in Spaces of Sequences Summed with Exponential Weights—Part 1: One-Sided Invertibility. Integr. Equ. Oper. Theory 82, 575–600 (2015). https://doi.org/10.1007/s00020-014-2207-0

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