Research interests: Hugo
Junghenn
My research is in the area of
analysis on semigroups. The subject has its origins in the work of H. Bohr
in the beginning of this century on almost periodic functions on the real
line. Since then the subject has grown enormously and now includes the
study of weakly almost periodic functions, almost automorphic functions,
distal functions and many other functions of ``almost periodic type'',
as well as semigroup representations, topological dynamics, and invariant
measures on compact semigroups. The unifying concept in the study of these
diverse areas is the right topological semigroup compactification. The
algebraic structure of this compactification plays an essential role in
determining the functional analytic properties of representations of the
underlying semigroup, the analytical properties of functions on semigroups,
and the topological dynamical properties of actions of the semigroup on
compact spaces. My research is concerned mainly with determining how each
of these disciplines sheds light on the others.
Selected Publications
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Distal compactifications
of semigroups, Trans. Amer. Math. Soc.
274 (1982), 379-397.
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Weakly almost periodic representations
of semigroups by Markov operators, Semigroup Forum 35 (1987)
195-205.
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Analysis on Semigroups: Function
Spaces, Compactifications, Representations, John Wiley and Sons, N.Y.
(1989) (334 pages). (with J.F. Berglund and P. Milnes).
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Direct sums of spaces of
functions on semigroups, Semigroup Forum
49 (1994) 115-123.
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Compactifications of N-fold
and infinite semidirect products of semigroups, Semigroup Forum 51
(1995) 31-45
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Compactifications of operator
semigroups. (To appear in Trans. Amer. Math. Soc.).