Displaying similar documents to “Extreme and exposed representing measures of the disk algebra”

Exposed points in the set of representing measures for the disc algebra

Alexander J. Izzo (1995)

Annales Polonici Mathematici

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It is shown that for each nonzero point x in the open unit disc D, there is a measure whose support is exactly ∂D ∪ {x} and that is also a weak*-exposed point in the set of representing measures for the origin on the disc algebra. This yields a negative answer to a question raised by John Ryff.

The L q spectra and Rényi dimension of generalized inhomogeneous self-similar measures

Przemysław Liszka (2014)

Open Mathematics

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Very recently bounds for the L q spectra of inhomogeneous self-similar measures satisfying the Inhomogeneous Open Set Condition (IOSC), being the appropriate version of the standard Open Set Condition (OSC), were obtained. However, if the IOSC is not satisfied, then almost nothing is known for such measures. In the paper we study the L q spectra and Rényi dimension of generalized inhomogeneous self-similar measures, for which we allow an infinite number of contracting similarities and...