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Keywords:
complex symmetry; weighted composition operator; Hardy space
complex symmetry; weighted composition operator; Hardy space
Summary:
This paper identifies a class of complex symmetric weighted composition operators on $H^2(\mathbb {D})$ that includes both the unitary and the Hermitian weighted composition operators, as well as a class of normal weighted composition operators identified by Bourdon and Narayan. A characterization of algebraic weighted composition operators with degree no more than two is provided to illustrate that the weight function of a complex symmetric weighted composition operator is not necessarily linear fractional.
References:
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