Vector-valued Ruelle operator with weakly contractive IFS |
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Authors: | Yuan-Ling Ye |
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Institution: | School of Mathematical Sciences, South China Normal University, Guangzhou 510631, PR China |
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Abstract: | The vector-valued Ruelle operator defined by contractive iterated function systems (IFS) was discussed by the author Y.L. Ye, Vector-valued Ruelle operator, J. Math. Anal. Appl. 299 (2004) 341-356]. In this paper we consider vector-valued Ruelle operators defined by weakly contractive IFS. And, a vector-valued analogue of the Ruelle-Perron-Frobenius theorem for the scalar Ruelle operator is set up. Our theorem gives a sufficient condition for the vector-valued Ruelle operator to be quasi-compact. Under this sufficient condition, we prove that the rate of convergence of the iterated operators is exponential. |
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Keywords: | Vector-valued Ruelle operator Weakly contractive IFS Quasi-compact Perron-Frobenius property |
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