Regular subspaces of a quaternionic Hilbert space from quaternionic   Hermite polynomials and associated coherent states
  We define quaternionic Hermite polynomials by analogy with two families of complex Hermite polynomials. As in the complex case, these polynomials consatitute orthogonal families of vectors in ambient quaternionic $L^2$-spaces. Using these polynomials, we then define regular and anti-regular subspaces of these $L^2$-spaces, the associated reproducing kernels and the ensuing quaternionic coherent states. 
K. Thirulogasanthar and S. Twareque Ali
math-ph math.MP quant-ph