TY - Type of reference
TI - [Forthcoming] Explicit formulas of the heat kernel on the quaternionic projective spaces
AU - Ali Hafoud
AU - Allal Ghanmi
AB - We consider the heat equation on the quaternionic projective space $$$P_{n}(ℍ)$$$, and we establish two formulas for the heat kernel, a series expansion involving Jacobi polynomials, and an integral representation involving a $$$\theta$$$-function. More precisely, using the quaternonic Hopf fibration and the explicit integral representation of the heat kernel on the complex projective space $$$P_{2n+1}(ℂ)$$$, as well as an integral representation of Jacobi polynomials in terms of Gegenbauer polynomials, we give an explicit integral representation of the heat kernel on the $$$n$$$-quaternionic projective space. We also establish an explicit series expansion of the heat kernel in terms of the Jacobi polynomials. Moreover, we derive an explicit formula of the heat kernel on the sphere $$$S^4$$$.
DO -
JF - Advances in Pure and Applied Mathematics
KW - Heat equation, Heat kernel, Quaternionic projective space, Hopf fibration, Jacobi polynomials, Heat equation, Heat kernel, Quaternionic projective space, Hopf fibration, Jacobi polynomials,
L1 -
LA - en
PB - ISTE OpenScience
DA - 2021/08/9
SN - 1869-6090
TT - [Forthcoming] Formules explicites du noyau de la chaleur sur les espaces projectifs des quaternions
UR - https://www.openscience.fr/Explicit-formulas-of-the-heat-kernel-on-the-quaternionic-projective-spaces
IS - Forthcoming papers

VL - 13
ER -