Positive Definite Temperature Functions On The Euclidean Motion Group
DOI:
https://doi.org/10.60787/jnamp.vol69no1.465Keywords:
Euclidean Motion Group , Invariant differential operator, Distribution, Universal enveloping algebra, Spherical functionsAbstract
Let SE(2) be a two dimensional Euclidean motion group realized as the semi-direct product of R2 and SO(2). The Fourier transform of spherical function on SE(2) and its boundedness are presented. Furthermore, a description of temperature function and positive definite temperature functions on SE(2) is presented, among other things. This temperature function is realized as the positive definite solution of the Laplace-Beltrami operator on SE(2).
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