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An implicit canonical equation in Hilbert space

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Abstract

The differential equation ɛx=G(t)x, 0⩽t⩽T, where ɛ and G(t) are bounded linear operators, is examined in the complex Hilbert space conditions are found under which this equation is reducible to the canonical equation by a change of variables.

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Literature cited

  1. Yu. L. Daletskii and M. G. Krein, Stability of Solutions of Differential Equations in Banach Space, Am. Math. Soc., Providence (1974).

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Authors and Affiliations

  1. Technical Institute of Logging, Voronezh

    S. G. Krein & E. O. Utochkina

Authors
  1. S. G. Krein
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  2. E. O. Utochkina
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 3, pp. 388–390, May–June, 1990.

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Krein, S.G., Utochkina, E.O. An implicit canonical equation in Hilbert space. Ukr Math J 42, 345–347 (1990). https://doi.org/10.1007/BF01057021

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  • DOI: https://doi.org/10.1007/BF01057021

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