Abstract
The celebrated Cauchy singular integral operator on a Jordan curve, or more precisely, its 1-periodic counterpart is perhaps the most important brick in the theory of periodic integral and pseudodifferential operators. In this chapter, we first treat the Cauchy singular operators in the Hölder spaces C α(Γ) and after that we extend the results to L 2(Γ). In the next chapters we consider the Cauchy singular operator in a scale of 1-periodic Sobolev spaces H λ, λ ∈ ℝ, with H 0 corresponding to L 2(Γ).KeywordsCompact OperatorSingular Integral EquationPseudodifferential OperatorJordan CurveSingular Integral OperatorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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