The Analogues of Entropy and of Fisher's Information Measure in Free Probability Theory III: The Absence of Cartan Subalgebras.
D. Voiculescu (1996)
Geometric and functional analysis
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D. Voiculescu (1996)
Geometric and functional analysis
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Giurgescu, Patricia (2000)
International Journal of Mathematics and Mathematical Sciences
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Dan Voiculescu (1994)
Inventiones mathematicae
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Jan Goncerzewicz, Danielle Hilhorst (2000)
Banach Center Publications
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% We study the large time behaviour of entropy solutions of the Cauchy problem for a possibly degenerate nonlinear diffusion equation with a nonlinear convection term. The initial function is assumed to have bounded total variation. We prove the convergence of the solution to the entropy solution of a Riemann problem for the corresponding first order conservation law.
Erling Stormer (1992)
Inventiones mathematicae
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Choda, Marie (2010)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Richard Miles (2008)
Fundamenta Mathematicae
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This paper is concerned with the entropy of an action of a countable torsion-free abelian group G by continuous automorphisms of a compact abelian group X. A formula is obtained that expresses the entropy in terms of the Mahler measure of a greatest common divisor, complementing earlier work by Einsiedler, Lind, Schmidt and Ward. This leads to a uniform method for calculating entropy whenever G is free. In cases where these methods do not apply, a possible entropy formula is conjectured....
Chakrabarti, C.G., Chakrabarty, Indranil (2005)
International Journal of Mathematics and Mathematical Sciences
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Emmanuel Germain (2007)
Annales mathématiques Blaise Pascal
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We present here two non-commutative situations where dynamical entropy estimates are possible. The first result is concerned with automorphisms of cross-products by an exact group that commute with the group action and generalizes the result known for amenable groups. The second is about continuous fields of C-algebras and -automorphisms. Each result relies on explicit factorization via matrices.
Gselmann, Eszter (2008)
Banach Journal of Mathematical Analysis [electronic only]
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