On the braided Fourier transform in the n-dimensional quantum space

الأصل · EN

We work out a theory of integrability on the braided covector Hopf algebra and braided vector Hopf algebra of type Aₙ as introduced by Kempf and Majid. Starting by their definition of braided Fourier transform we prove n-dimensional analogues to results by Koornwinder expressing the correspondence between products of q²-Gaussians times monomials and products of q²-Gaussians times q²-Hermite polynomials under the transform. We invert the correspondence finding a suitable inverse to the transform, different from that by Kempf and Majid (our integral is not bosonic) and we show that in this case the (q-)Plancherel measure will depend on the parity of the generalized functions that we are transforming.