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Entropy as an integral operator: Erratum and modification

In: Mathematica Slovaca, vol. 70, no. 5
Mehdi Rahimi

Details:

Year, pages: 2020, 1183 - 1188
Keywords:
entropy, invariant, entropy kernel operator
About article:
In [\uppercase{Rahimi, M.}: \textit{Entropy as an integral operator}, Math. Slovaca \textbf{69}(1) (2019),\linebreak 139–146], we assigned an integral operator on a Hilbert space to any topological dynamical system of finite entropy and stated the entropy of the system in terms of the spectrum of the defined operator. Unfortunately, there is a mistake in the proof of the main theorem of the paper which makes the result incorrect. So, we can not extract the entropy of a topological dynamical system in terms of the spectrum of the introduced operator. In this note, we modify the main theorem of [RR] by giving a modification to the proof of the theorem. Then, replacing the integral operator introduced in [RR] by another linear operator, we will state the entropy of the system in terms of the spectrum of the new operator.
How to cite:
ISO 690:
Rahimi, M. 2020. Entropy as an integral operator: Erratum and modification. In Mathematica Slovaca, vol. 70, no.5, pp. 1183-1188. 0139-9918. DOI: https://doi.org/DOI: 10.1515/ms-2017-0423

APA:
Rahimi, M. (2020). Entropy as an integral operator: Erratum and modification. Mathematica Slovaca, 70(5), 1183-1188. 0139-9918. DOI: https://doi.org/DOI: 10.1515/ms-2017-0423
About edition:
Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Published: 27. 9. 2020