Abstract
ABSTRACTIn this article, we extend the Stockwell transform to the space of all square integrable quaternion-valued functions on the real line, using the convolution of quaternion-valued functions. We prove that the extended Stockwel transform satisfies the Parseval's formula, inversion formula, and uncertainty principle. We also characterize the range of the Stockwell transform on and prove a convolution theorem for the extended Stockwell transform. Applying the convolution theorem, we extend the transform to a suitable Boehmian space of quaternion-valued functions.
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