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On the analogue of the formula \(\cos t = e^{it} + e^{-it}\) for operator cosine functions. (English) Zbl 0594.47035

Summary: The aim of this paper is to present some connections between one parameter strongly continuous groups of linear bounded operators on a Banach space and operator cosine functions. We get a formula which is analogous to the classical one: \(\cos t = e^{it}+e^{-it}\).

MSC:

47D03 Groups and semigroups of linear operators
47D99 Groups and semigroups of linear operators, their generalizations and applications
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