Abstract
The present paper is devoted to the study of equivariant embeddings of the n-dimensional space into a Hilbert space. We consider a representation of a group of similarities. The existence of a cocycle for this representation implies the existence of an isometric embedding of a metric group into the Hilbert space. Then we describe all cocycles of a representation of the additive group of real numbers and construct an embedding of the n-dimensional space with metric d(x,y)=|x-y|α into the Hilbert space. Bibliography: 5 titles.
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Gorbulsky, M. Equivariant Embeddings of the n-Dimensional Space into a Hilbert Space. Journal of Mathematical Sciences 121, 2326–2329 (2004). https://doi.org/10.1023/B:JOTH.0000024614.98313.86
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DOI: https://doi.org/10.1023/B:JOTH.0000024614.98313.86