On the Fourier Analysis for L2 Operator-Valued Functions
We endow the set of square integrable operator-valued functions on a locally compact group with a pre-Hilbert module structure and define the ρ-Fourier transform for such functions. We also describe the Fourier transform of Hilbert-Schmidt operator-valued function on compact groups.
KeywordsFourier transform Hilbert module Hilbert-Schmidt operator Topological groups
The co-author Yaogan Mensah would like to thank the Third World Academy of Science (TWAS) for its financial support (Fellowship for Research and Advanced Training, FR Number: 3240257263). He also thanks Prof. K. B. Sinha from the Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore (India) for introducing him to some aspects of operator theory.
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