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Invertibility Conditions for Second-Order Differential Operators in the Space of Continuous Bounded Functions

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Abstract

We prove the invertibility of second-order differential operators with constant operator coefficients acting on the Banach space of bounded continuous functions on the real line under the condition that they are uniformly injective (in particular, left invertible) or surjective (in particular, right invertible). We show that if these operators are considered on the space of periodic functions, then the unilateral invertibility does not imply the invertibility of such operators. We obtain criteria for the injectivity, surjectivity, and invertibility of differential operators on the space of periodic functions.

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Authors and Affiliations

  1. Voronezh State University, Voronezh, 394006, Russia

    A. G. Baskakov, L. Yu. Kabantsova & T. I. Smagina

  2. Khetagurov North Ossetian State University, Vladikavkaz, 362025, Russia

    A. G. Baskakov

Authors
  1. A. G. Baskakov
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  2. L. Yu. Kabantsova
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  3. T. I. Smagina
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Correspondence to A. G. Baskakov.

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Original Russian Text © A.G. Baskakov, L.Yu. Kabantsova, T.I. Smagina, 2018, published in Differentsial’nye Uravneniya, 2018, Vol. 54, No. 3, pp. 292–301.

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Baskakov, A.G., Kabantsova, L.Y. & Smagina, T.I. Invertibility Conditions for Second-Order Differential Operators in the Space of Continuous Bounded Functions. Diff Equat 54, 285–294 (2018). https://doi.org/10.1134/S0012266118030011

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  • DOI: https://doi.org/10.1134/S0012266118030011

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