Complex Symmetric Toeplitz Operators

This paper aims to study when a Toeplitz operator T-phi on the Hardy space H-2 of the unit disk is complex symmetric, that is, T-phi admits a symmetric matrix representation relative to some orthonormal basis of H-2. For certain trigonometric symbols., we give necessary and sufficient conditions for T-phi to be complex symmetric. In particular, we show that their complex symmetry coincides with the property "unitary equivalence to their transposes".