Abstract
It is proved that the Laplace transform establishes a bijection between a class of resolvents (V α ) α >0 and a class of semi-groups Φ of kernels, acting on an abstract ordered convex cone. The compactness (in some weak topology) of the closed convex envelopes of the trajectories: Φ(t, x), t > 0, resp. of (nV n )kx, n, k ∈ ȑ, plays a central role in these results.
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Popa, E. A Hille–Yosida Type Theorem in Ordered Convex Cones. Positivity 10, 555–571 (2006). https://doi.org/10.1007/s11117-005-0014-1
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DOI: https://doi.org/10.1007/s11117-005-0014-1