Entropy and n-widths of operators in Banach spaces
Bernd Carl (1989)
Banach Center Publications
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Bernd Carl (1989)
Banach Center Publications
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Carl, Bernd, Edmunds, David E. (2001)
Journal of Inequalities and Applications [electronic only]
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Thomas Kühn (1984)
Studia Mathematica
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Bernd Carl, Hans Triebel (1980)
Mathematische Annalen
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Bernd Carl, Thomas Kühn (1984)
Mathematische Annalen
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V. P. Belavkin, P. Staszewski (1982)
Annales de l'I.H.P. Physique théorique
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Gselmann, Eszter (2008)
Banach Journal of Mathematical Analysis [electronic only]
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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.
Brunon Kamiński, José de Sam Lazaro (2000)
Colloquium Mathematicae
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We investigate the properties of the entropy and conditional entropy of measurable partitions of unity in the space of essentially bounded functions defined on a Lebesgue probability space.
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.
Philippe Bénilan, Jose Carrillo, Petra Wittbold (2000)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Susana Domingues de Moura
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We study spaces of generalised smoothness of Besov and Triebel-Lizorkin type. In particular, we get characterisations by local means, atomic and subatomic representations. These results are applied to estimate the entropy numbers of compact embeddings between function spaces on fractals. Due to Carl's inequality this is useful in the study of the behaviour of eigenvalues in problems which correspond to the vibrations of a drum, the whole mass of which is concentrated on a fractal subset...