Abstract
In this article, we present the abstract harmonic analysis aspects of the operator-valued continuous Gabor transform (CGT) on second countable, non-unimodular, and type I locally compact groups. We show that the operator-valued continuous Gabor transform CGT satisfies a Plancherel formula and an inversion formula. As an example, we study these results on the continuous affine group.
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Ghaani Farashahi, A. Operator-Valued Continuous Gabor Transforms over Non-unimodular Locally Compact Groups. Mediterr. J. Math. 14, 136 (2017). https://doi.org/10.1007/s00009-017-0936-4
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DOI: https://doi.org/10.1007/s00009-017-0936-4