Abstract
We are concerned with extensions of locally defined continuous and positive definite (p.d.) functions F on Lie groups, say G, but some results apply to locally compact groups as well. However in the case of locally compact Abelian groups, we have stronger theorems, due to the powerful Fourier analysis theory in this specific setting.
Nowadays, group theoretical methods — especially those involving characters and representations, pervade all branches of quantum mechanics.
— George Mackey
The universe is an enormous direct product of representations of symmetry groups.
— Hermann Weyl
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Jorgensen, P., Pedersen, S., Tian, F. (2016). The Case of More General Groups. In: Extensions of Positive Definite Functions. Lecture Notes in Mathematics, vol 2160. Springer, Cham. https://doi.org/10.1007/978-3-319-39780-1_3
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DOI: https://doi.org/10.1007/978-3-319-39780-1_3
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