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CMFD, 2006, Volume 15, Pages 5–18 (Mi cmfd35)  

Variational principles for spectral radii of positive functional operators

A. B. Antonevichab

a Belarusian State University
b University of Bialystok

Abstract: Functional operators, i.e., sums of weighted shift operators generated by various maps, are considered. For functional operators with positive coefficients, variational principles for spectral radii are obtained. These principles say that the logarithm of the spectral radius is the Legendre transform of a certain convex functional $T$ defined on the set of probability vector-valued measures and depending on the original dynamical system and the functional space considered. In the subexponential case, we obtain the combinatorial structure of the functional $T$ with the help of the corresponding random walk process constructed according to the dynamical system.

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English version:
Journal of Mathematical Sciences, 2008, 149:4, 1345–1358

Bibliographic databases:

UDC: 517.983.23+517.984.5

Citation: A. B. Antonevich, “Variational principles for spectral radii of positive functional operators”, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 1, CMFD, 15, PFUR, M., 2006, 5–18; Journal of Mathematical Sciences, 149:4 (2008), 1345–1358

Citation in format AMSBIB
\Bibitem{Ant06}
\by A.~B.~Antonevich
\paper Variational principles for spectral radii of positive functional operators
\inbook Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14--21, 2005). Part~1
\serial CMFD
\yr 2006
\vol 15
\pages 5--18
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd35}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2336424}
\transl
\jour Journal of Mathematical Sciences
\yr 2008
\vol 149
\issue 4
\pages 1345--1358
\crossref{https://doi.org/10.1007/s10958-008-0068-2}


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