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December 1998 Fredholm Determinant for Piecewise Linear Transformations on a Plane
Makoto MORI
Tokyo J. Math. 21(2): 477-510 (December 1998). DOI: 10.3836/tjm/1270041829


Certain piecewise linear expanding maps on a finite union of polygons in $\mathbf{R}^2$ are considered. The Perron-Frobenius operator associated with a map is considered on a locally convex linear space which is an extension of the space of bounded variation functions, and the spectrum of it is determined by Fredholm matrices. New signed symbolic dynamics are defined by using screens, and the Fredholm matrices are constructed by renewal equations on this signed symbolic dynamics.


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Makoto MORI. "Fredholm Determinant for Piecewise Linear Transformations on a Plane." Tokyo J. Math. 21 (2) 477 - 510, December 1998.


Published: December 1998
First available in Project Euclid: 31 March 2010

zbMATH: 0919.58023
MathSciNet: MR1663626
Digital Object Identifier: 10.3836/tjm/1270041829

Rights: Copyright © 1998 Publication Committee for the Tokyo Journal of Mathematics


Vol.21 • No. 2 • December 1998
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