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arXiv · 1206.3684

Regular subspaces of a quaternionic Hilbert space from quaternionic Hermite polynomials and associated coherent states

K. Thirulogasanthar·S. Twareque Ali
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Abstract

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.

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K. Thirulogasanthar, S. Twareque Ali. 2012-06-16. Regular subspaces of a quaternionic Hilbert space from quaternionic Hermite polynomials and associated coherent states. https://doi.org/10.1063/1.4774963

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