This analysis constructs spherical Fourier multipliers on Gelfand pairs in the quaternionic heisenberg group, indicating new properties of automorphisms.
Let Hq denote the quaternionic Heisenberg group with R⁴³ stratification and K a compact subgroup of Automorphism. We construct the spherical Fourier multiplier related to a Gelfand Pairs on the Quaternionic Heisenberg group Hq via the motion group G=K Hq of Hq, where K Hq is the semidirect product of Hq and its compact subgroup of automorphism K∈ Aut(Hq).
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Ariyo et al. (2025) studied this question.
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