On the braided Fourier transform in the ndimensional quantum space
Abstract
We work out a theory of integrability on the braided covector Hopf algebra and braided vector Hopf algebra of type A_n as introduced by Kempf and Majid. Starting by their definition of braided Fourier transform we prove ndimensional analogues to results by Koornwinder expressing the correspondence between products of q^2Gaussians times monomials and products of q^2Gaussians times q^2Hermite 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 1998
 DOI:
 10.48550/arXiv.math/9810011
 arXiv:
 arXiv:math/9810011
 Bibcode:
 1998math.....10011C
 Keywords:

 Quantum Algebra;
 Classical Analysis and ODEs
 EPrint:
 Plain TeX, 39 pages