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On the asymptotic behavior of certain infinite-dimensional recurrence sequences

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Abstract

Under certain conditions imposed on an operatorB, we obtain criteria of boundedness of sequencesx n+1=Ax n +Bb n , n>0, for anyx 0 and bounded {b n ,n≥ 0} in infinite-dimensional spaces. The results are given in terms of spectral properties of the operatorA.

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References

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Authors and Affiliations

  1. Kiev University, Kiev

    Yu. V. Tomilov

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  1. Yu. V. Tomilov
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 133–137, January, 1995.

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Tomilov, Y.V. On the asymptotic behavior of certain infinite-dimensional recurrence sequences. Ukr Math J 47, 157–162 (1995). https://doi.org/10.1007/BF01058809

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  • DOI: https://doi.org/10.1007/BF01058809

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