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Functionals-preserving cosine families generated by Laplace operators in C[0,1]

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  • Let \( C[0,1] \) be the space of continuous functions on the unit interval \( [0,1] \). A cosine family $\{C(t), t \in \mathbb{R}\}$ in $C[0,1]$ is said to be Laplace-operator generated, if its generator is a restriction of the Laplace operator $L\colon f \mapsto f''$ to a suitable subset of $C^2[0,1].$ The family is said to preserve a functional $F \in (C[0,1])^*$ if for all $f \in C[0,1]$ and $t \in \mathbb{R}, $ $FC(t)f = Ff.$ We study a class of pairs of functionals such that for each member of this class there is a unique Laplace-operator generated cosine family that preserves both functionals in the pair.
    Mathematics Subject Classification: 47D06, 47D09.


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