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Spectral properties of cosine operator functions. (English) Zbl 0675.47029
Summary: Let A be the generator of a cosine function C t , t in a Banach space X; we shall connect the existence and uniqueness of a T- periodic mild solution of the equation u '' =Au+f with the spectral property 1ρ(C T ) and, in case X is a Hilbert space, also with spectral properties of A.

47D03(Semi)groups of linear operators
34G10Linear ODE in abstract spaces
47D99Algebraic systems of linear operators
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