Geodesic
Cosine Representations of Abelian *-Semigroups and Generalized Cosine Operator Functions
Canadian journal of mathematics, Tome 30 (1978) no. 3, pp. 474-482

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In the following R will denote the real numbers, for a Hilbert space H, B(H) and L(H) will denote the collections of bounded linear operators on H and linear, but not necessarily bounded, operators on H respectively. Cosine Operator Functions, namely functions C:R ⟶ B(H) which satisfy D'Alembert's functional equation (1) and (2) 
Faulkner, G. D.; Shonkwiler, R. W. Cosine Representations of Abelian *-Semigroups and Generalized Cosine Operator Functions. Canadian journal of mathematics, Tome 30 (1978) no. 3, pp. 474-482. doi: 10.4153/CJM-1978-042-3
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