Equivariant Embeddings of the n-Dimensional Space into a Hilbert Space |
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Authors: | M Gorbulsky |
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Institution: | (1) St.Petersburg State University, Russia |
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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| into the Hilbert space. Bibliography: 5 titles. |
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