Generalized inverses and solution of equations with Toeplitz plus Hankel operators (Q334764)

For \(1<p<\infty\), let \(H^p(\mathbb{T})\) denote the Hardy space on the unit circle \(\mathbb{T}\). Assuming that \(a, b\in L^\infty(\mathbb{T})\) and \(a(t)a(1/t) = b(t) b(1/t)\), \(t\in \mathbb{T}\), the authors develop two analytic methods to solve the following Toeplitz plus Hankel equation: \[ (T_a +H_b)\varphi = f, \quad f\in H^p(\mathbb{T}). \] Both constructions use generalized inverses and Wiener-Hopf factorizations. The first one is related to a Toeplitz operator \(T_{V(a, b)}\), where \(V(a, b)\) is a triangular matrix-valued function; the second one uses generalized inverses of the initial operator \(T_a +H_b\).