Abstract
The iterates of an operator and their limit are studied in ergodic theory, approximation theory and other related fields. In this paper we continue the study of iterates of certain Markov operators acting on C[0,1]. We provide new sufficient conditions under which a Markov operator L is uniquely ergodic, i.e., it admits a unique invariant probability measure \(\nu \). The determination of \(\nu \) is reduced to solving an algebraic system of linear equations. Then \(\nu \) is used in order to express the limit of the iterates of L. Another useful tool in this study is the eigenstructure of L. The general results are applied to several families of classical Markov operators.
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This work was supported by a Hasso Plattner Excellence Research Grant (LBUS-HPI-ERG-2020-04), financed by the Knowledge Transfer Center of the Lucian Blaga University of Sibiu.
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Acu, AM., Heilmann, M. & Rasa, I. Eigenstructure and iterates for uniquely ergodic Kantorovich modifications of operators II. Positivity 25, 1585–1599 (2021). https://doi.org/10.1007/s11117-021-00832-7
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DOI: https://doi.org/10.1007/s11117-021-00832-7