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

Published online by Cambridge University Press:  20 November 2018

G. D. Faulkner  and
R. W. Shonkwiler
G. D. Faulkner
Affiliation:
North Carolina State University, Raleigh, North Carolina
R. W. Shonkwiler
Affiliation:
Georgia Institute of Technology, Atlanta, Georgia
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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)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 3 , 01 June 1978 , pp. 474 - 482
Copyright
Copyright © Canadian Mathematical Society 1978

References

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