We prove Beurling's theorem for rank $1$ Riemannian symmetric spaces and relate its consequences with the characterization of the heat kernel of the symmetric space.

Keywords:

Beurling's Theorem, Riemannian symmetric spaces, uncertainty principle Beurling's Theorem, Riemannian symmetric spaces, uncertainty principle

MSC Classifications:

22E30, 43A85 show english descriptions Analysis on real and complex Lie groups [See also 33C80, 43-XX]
Analysis on homogeneous spaces 22E30 - Analysis on real and complex Lie groups [See also 33C80, 43-XX]
43A85 - Analysis on homogeneous spaces

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