On the modified entropy equation.
Gselmann, Eszter (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Gselmann, Eszter (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Edmunds D. E., Haroske D.
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AbstractWe establish the sharpness of the embedding of certain Besov and Triebel-Lizorkin spaces in spaces of Lipschitz type. In particular, this proves the sharpness of the Brézis-Wainger result concerning the “almost” Lipschitz continuity of elements of the Sobolev space , where 1 < p < ∞. Upper and lower estimates are obtained for the entropy numbers of related embeddings of Besov spaces on bounded domains. CONTENTSIntroduction...........................................................51....
Bartosz Frej (2006)
Fundamenta Mathematicae
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The paper deals with the notion of entropy for doubly stochastic operators. It is shown that the entropy defined by Maličky and Riečan in [MR] is equal to the operator entropy proposed in [DF]. Moreover, some continuity properties of the [MR] entropy are established.
Philippe Bénilan, Jose Carrillo, Petra Wittbold (2000)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Carl, Bernd, Edmunds, David E. (2001)
Journal of Inequalities and Applications [electronic only]
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Kyewon Koh Park, Uijung Lee (2004)
Studia Mathematica
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Topological and metric entropy pairs of ℤ²-actions are defined and their properties are investigated, analogously to ℤ-actions. In particular, mixing properties are studied in connection with entropy pairs.
Chakrabarti, C.G., De, Kajal (2000)
International Journal of Mathematics and Mathematical Sciences
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Inder Jeet Taneja (1977)
Annales Polonici Mathematici
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Fumio Hiai, Dénes Petz (2007)
Banach Center Publications
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A new expression as a certain asymptotic limit via "discrete micro-states" of permutations is provided for the mutual information of both continuous and discrete random variables.
Francisco Balibrea (2015)
Topological Algebra and its Applications
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Discrete dynamical systems are given by the pair (X, f ) where X is a compact metric space and f : X → X a continuous maps. During years, a long list of results have appeared to precise and understand what is the complexity of the systems. Among them, one of the most popular is that of topological entropy. In modern applications other conditions on X and f have been considered. For example X can be non-compact or f can be discontinuous (only in a finite number of points and with bounded...
Young-Ho Ahn, Dou Dou, Kyewon Koh Park (2010)
Studia Mathematica
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Recently the notions of entropy dimension for topological and measurable dynamical systems were introduced in order to study the complexity of zero entropy systems. We exhibit a class of strictly ergodic models whose topological entropy dimensions range from zero to one and whose measure-theoretic entropy dimensions are identically zero. Hence entropy dimension does not obey the variational principle.
Chakrabarti, C.G., Chakrabarty, Indranil (2005)
International Journal of Mathematics and Mathematical Sciences
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Collet, P. (1998)
Documenta Mathematica
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Dawid Huczek (2012)
Colloquium Mathematicae
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We prove that an invertible zero-dimensional dynamical system has an invariant measure of maximal entropy if and only if it is an extension of an asymptotically h-expansive system of equal topological entropy.
Bernd Carl (1989)
Banach Center Publications
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Fumio Hiai, Takuho Miyamoto (2010)
Banach Center Publications
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A new concept of mutual pressure is introduced for potential functions on both continuous and discrete compound spaces via discrete micro-states of permutations, and its relations with the usual pressure and the mutual information are established. This paper is a continuation of the paper of Hiai and Petz in Banach Center Publications, Vol. 78.
Christian Mauduit, Carlos Gustavo Moreira (2010)
Acta Arithmetica
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François Blanchard (1993)
Bulletin de la Société Mathématique de France
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