Let \(K_\Omega(\cdot, z)\) be the Bergman kernel for a domain \(\Omega\) in \(\mathbb{C}^n\). Let \(H^\infty(\Omega)\) be the space of bounded holomorphic functions on \(\Omega\). For \(f\in L^2(\Omega)\), define a map \(H_f: H^\infty(\Omega)\to A^2(\Omega)^{\perp}\subset L^2(\Omega)\) by \(H_f(g):= (I- P)(fg)\), where \(P= P_\Omega: L^2(\Omega)\to A^2(\Omega)\) is the orthogonal projection map. K. Stroethoff [J. Oper. Theory 23, No. 1, 153-170 (1990; Zbl 0723.47018)] investigated the unit ball \(B_n\) in \(\mathbb{C}^n\), pointed out the importance of a formula for the image under \(H_f\) of the \(K_{B_n}(\cdot, z)\) for \(z\in B_n\) and showed a crucial role of the Möbius functions. We will investigate its generalization for a bounded Hankel operator on a symmetric domain with rank one.
For the entire collection see [Zbl 0903.00037].