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On the quaternionic short-time Fourier and Segal-Bargmann transforms (2009.00073v1)
Published 31 Aug 2020 in math.CV
Abstract: In this paper, we study a special one dimensional quaternion short-time Fourier transform (QSTFT). Its construction is based on the slice hyperholomorphic Segal-Bargmann transform. We discuss some basic properties and prove different results on the QSTFT such as Moyal formula, reconstruction formula and Lieb's uncertainty principle. We provide also the reproducing kernel associated to the Gabor space considered in this setting.