Some Remarks on Projective Representations of Compact Groups and Frames

Abstract

In this paper, we study continuous frames with symmetries from projective representations of compact groups. In particular, we study maximal spanning vectors in detail and we prove the existence of maximal spanning vectors for irreducible projective representations of compact abelian groups by a dimension counting method.

Keywords

Continuous frame / Fourier transform / Maximal spanning vector / Projective representation / The Peter–Weyl theorem / 20C25 / 42C15 / 43A77

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Funding

NSFC(12071221)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature