Erratum to ‘‘Entropy for group endomorphisms and homogeneous spaces”

Metric Entropy of Homogeneous Spaces

For a (compact) subset K of a metric space and ε > 0, the covering number N(K, ε) is defined as the smallest number of balls of radius ε whose union covers K. Knowledge of the metric entropy, i.e., the asymptotic behaviour of covering numbers for (families of) metric spaces is important in many areas of mathematics (geometry, functional analysis, probability, coding theory, to name a few). In t...

Zero - Entropy Affine Maps on Homogeneous Spaces

Frames and Homogeneous Spaces

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

Convolution and Homogeneous Spaces

Homogeneous Spaces of the Lorentz Group

We present a classification, up to isomorphisms, of all the homogeneous spaces of the Lorentz group with dimension lower than six. At the same time, we classify, up to conjugation, all the non-discrete closed subgroup of the Lorentz group and all the subalgebras of the Lorentz Lie algebra. We also study the covariant mappings between some pairs of homogeneous spaces. This exercise is done witho...