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

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.

References in corpus (2)

• A new series expansion for slice regular functions
• A Brief History of Quaternions and of the Theory of Holomorphic Functions of Quaternionic Variables

Cited by in corpus (8)

• A Representation of Weyl-Heisenberg Lie Algebra in the Quaternionic Setting
• Coherent state Quantization of quaternions
• Discrete frames on finite dimensional quaternion Hilbert spaces
• On the dimensions of the oscillator algebras induced by orthogonal polynomials
• S-spectrum and Associated Continuous Frames on Quaternionic Hilbert Spaces
• Perturbation of Continuous Frames on Quaternionic Hilbert Spaces
• Squeezed states in the quaternionic setting
• Generalized 2D Laguerre polynomials and their quaternionic extensions