MATERIAL SYMMETRY RESTRICTIONS FOR CERTAIN LOCALLY COMPACT SYMMETRY GROUPS.
BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS
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For compact symmetry groups, Wineman and Pipkin have shown that the canonical forms obtained for form-invariant polynomials apply to all form-invariant functions. By a topological ergodic theorem, we construct a group average for bounded representations of those locally compact groups we call mean-ergodic, and for these groups thereby show that the form-invariant polynomials are dense among the form-invariant continuous functions. For representations with closed S-orbits we can characterize all invariant functions, and for Lindelof such groups we can characterize all form-invariant functions, thereby showing again under broader hypotheses that integrity bases are functional bases. Author
- Theoretical Mathematics