Abstract
We give explicit formulas for the adjoint, product and inverse of a bounded pseudo-differential operator in terms of its symbol on a compact and Hausdorff group. As applications we give necessary and sufficient conditions to insure that a bounded pseudo-differential operator on a compact and Hausdorff group G is self-adjoint, normal, and unitary on L2(G), and invertible on Lp(G) for 1 ≤ p < ∞.
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