Displaying similar documents to “The noncommutative Hilbert transform approach to free entropy”

Large time behaviour of a class of solutions of second order conservation laws

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.

The entropy of algebraic actions of countable torsion-free abelian groups

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....

Non-commutative entropy computations for continuous fields and cross-products

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 C ( X ) -automorphisms. Each result relies on explicit factorization via matrices.