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Functional calculus of operators with heat kernel bounds on non-doubling manifolds with ends

Functional calculus of operators with heat kernel bounds on non-doubling manifolds with ends

Let ∆ be the Laplace-Beltrami operator acting on a non-doubling manifold with two ends R m ♯R n with m > n ≥ 3. Let h t (x, y) be the kernels of the semigroup e -t∆ generated by ∆.We say that a non-negative self-adjoint operator L on L 2 …