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On frequently hypercyclic \(C\)-distribution cosine functions in Fréchet spaces. (English) Zbl 1454.47013

Summary: In this paper, we analyse frequently hypercyclic \(C\)-distribution cosine functions in separable infinite-dimensional complex Fréchet spaces. The notion of frequent hypercyclicity seems to be new even for cosine operator functions in separable infinite-dimensional Banach spaces (real or complex). Our results, formulated also in terms of global fractionally integrated \(C\)-cosine functions, are illustrated with several instructive examples.

MSC:

47A16 Cyclic vectors, hypercyclic and chaotic operators
47D09 Operator sine and cosine functions and higher-order Cauchy problems
47D60 \(C\)-semigroups, regularized semigroups
47D62 Integrated semigroups
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