Abstract
Abstract Let G be a compact Hausdorff group and let H be a closed subgroup of G. We introduce pseudo-differential operators with symbols on the homogeneous space G / H {G/H} . We present a necessary and sufficient condition on symbols for which these operators are in the class of Hilbert–Schmidt operators. We also give a characterization of and a trace formula for the trace class pseudo-differential operators on the homogeneous space G / H {G/H} .
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