We work out in detail a theory of integrability on the braided covector Hopf algebra and the braided vector Hopf algebra of type introduced by Majid. Using a braided Fourier transform very similar to the one defined by Kempf and Majid we obtain n-dimensional analogs of results by Koornwinder expressing the correspondence between products of the -Gaussian times monomials, and products of the -Gaussian times -Hermite polynomials under the transform. We invert the correspondence by finding a suitable inversion, different from the one of Kempf and Majid. We show that with this transforms, whenever the Plancherel measure will depend on the parity of the power series that we are transforming.
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1999
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