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\centerline{\bf ABSTRACT}
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\centerline{\bf
On the structure of strongly continuous one-parameter groups}
\centerline{\bf of multilinear functionals}

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\centerline{L.L. STACH\'O}
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Out main results are structure theorems for strongly continuous one-parameter
groups formed by surjective linear isometries of the space of bounded
N-linear functionals over smoothly normed complex Banach spaces,
in particular over Hilbert spaces.
Though the Hilbert case with $N=1$ factor is a natural
analogue to Stone's classical theorem, some
crucial arguments of the proof go back to probability theory. As a
consequence, we classify the strongly continuous one-parameter
automorphism groups of all infinite-dimensional Cartan factors of
Jordan theory. We reduce the investigation of the strongly
continuous one-parameter groups by non-linear holomorphic
automorphism of the unit ball in ${\cal L}(H,K)$ to the study of
some retarded ordinary differential equations.


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