On the Analyticity of the Schwarz Operator with Respect to a Curve [chapter]

Luca Preciso, Sergei Rogosin
2003 Factorization, Singular Operators and Related Problems  
We consider the Schwarz operator T[·, ·] which assigns to each pair (φ, f ), where φ is a plane curve and f is a real-valued function, a holomorphic function F in the domain D enclosed by φ such that boundary values of F coincide with f . We show that T[φ, f ] depends real analytically on (φ, f ) in a suitable sense and in a Schauder space setting and we compute the first variations of T with respect its variables.
doi:10.1007/978-94-017-0227-0_16 fatcat:dewt6sqtbvestphzqgj37kvcxm