On the Analyticity of the Schwarz Operator with Respect to a Curve

Luca Preciso () and Sergei Rogosin ()
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Luca Preciso: University of Padova
Sergei Rogosin: Belarusian State University

A chapter in Factorization, Singular Operators and Related Problems, 2003, pp 237-254 from Springer

Abstract: Abstract The classical Schwarz operator T[•, •, •] assigns to each triple (ø, f, w), where ø is a plane closed curve enclosing a simply connected domain D, f is a real-valued function of the boundary of D and w ∈ D, the unique holomorphic function F of D satisfying Re F = f on the boundary of D and Im F(w) = 0. We consider the modified Schwarz operator T *, T * [ø, p, w] ≡ T[ø, p o ø(−1) w]o ø, which assigns to each triple (ø, p, w) the composition of the classical Schwarz operator T valued in (ø, poø (−1), w) with the boundary curve ø. We show that T *. depends real analytically on its variables and compute the first differential of T *. Regularity of another type of modifications of the Schwarz operator T is studied too.

Keywords: Schwarz boundary value problem; nonlinear operators; simply connected domain; Schauder spaces; perturbation analysis (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-0227-0_16

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DOI: 10.1007/978-94-017-0227-0_16

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