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Cosine Representations of Abelian *-Semigroups and Generalized Cosine Operator Functions

  • G. D. Faulkner (a1) and R. W. Shonkwiler (a2)

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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:RB(H) which satisfy D'Alembert's functional equation

(1)

and

(2)

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References

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1. Kurepa, S., A cosine functional equation in Banach algebras, Acta. Sci. Math. 23 (1962), 255267.
2. Kurepa, S., A cosine functional equation in Hilbert space, Can. J. Math. 12 (1960), 45–50.
3. Kurepa, S., A cosine functional equation in n-dimensional vector space, Glasnik mat. fiz. ast. 13 (1958), 169189.
4. Nagy, B., On cosine operator functions in Banach spaces, Acta. Sci. Math. 36 (1974), 281289.
5. Sz.-Nagy, B., Extensions of linear transformations in hilbert space which extend beyond this space New York, (1960).
6. Sova, M., Cosine operator functions, Rozprawy Matematyczne XLIX (Warsaw, 1966).
7. Naimark, M. A., On a representation of additive operator set functions, CR (Doklady) Acad. Sci. USSR, 41 (1943), 359361.
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Cosine Representations of Abelian *-Semigroups and Generalized Cosine Operator Functions

  • G. D. Faulkner (a1) and R. W. Shonkwiler (a2)

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