Abstract
Let (M,g) be a n-dimensional Riemannian manifold. Then g allows us to define a σ-regular Borel measure μ g on M determined by a positive linear functional λ g :C 0(M)→ℝ, where C 0(M) is the space of continuous real valued functions defined on M with compact support, that is for each f ∈ C 0(M) with f ≥ 0 we have λ g(f) ≥ 0. Indeed, let (U,Ø) be a local chart on M with coordinates x 1 ,…,x n, i.e. x 1 =ξ 1°Ø,1≤i≤n, where ξ 1:ℝn→ℝ denotes the canonical projection.
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Craioveanu, M., Puta, M., Rassias, T.M. (2001). Canonical Differential Operators Associated to a Riemannian Manifold. In: Old and New Aspects in Spectral Geometry. Mathematics and Its Applications, vol 534. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2475-3_2
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DOI: https://doi.org/10.1007/978-94-017-2475-3_2
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