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 L 2(G), and invertible on L p(G) for 1 ≤ p < ∞.
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Acknowledgements
This work of the first-named author was supported by the International Visiting Research Traineeship (IVRT) sponsored by Professor M. W. Wong at York University in 2017. The research of the second-named author has been supported by the Natural Sciences and Engineering Research Council of Canada under Discovery Grant 0008562.
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Jamalpourbirgani, M., Wong, M.W. (2019). Characterizations of Self-Adjointness, Normality, Invertibility, and Unitarity of Pseudo-Differential Operators on Compact and Hausdorff Groups. In: Molahajloo, S., Wong, M. (eds) Analysis of Pseudo-Differential Operators. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-05168-6_4
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DOI: https://doi.org/10.1007/978-3-030-05168-6_4
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Publisher Name: Birkhäuser, Cham
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