Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T06:10:36.049Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Kurepa, S., A cosine functional equation in Banach algebras, Acta. Sci. Math. 23 (1962), 255–267.Google Scholar
2. Kurepa, S., A cosine functional equation in Hilbert space, Can. J. Math. 12 (1960), 45–50.Google Scholar
3. Kurepa, S., A cosine functional equation in n-dimensional vector space, Glasnik mat. fiz. ast. 13 (1958), 169–189.Google Scholar
4. Nagy, B., On cosine operator functions in Banach spaces, Acta. Sci. Math. 36 (1974), 281–289.Google Scholar
5. Sz.-Nagy, B., Extensions of linear transformations in hilbert space which extend beyond this space New York, (1960).Google Scholar
6. Sova, M., Cosine operator functions, Rozprawy Matematyczne XLIX (Warsaw, 1966).Google Scholar
7. Naimark, M. A., On a representation of additive operator set functions, CR (Doklady) Acad. Sci. USSR, 41 (1943), 359–361.Google Scholar