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- Singular_integral_operators_on_closed_curves abstract "In mathematics, singular integral operators on closed curves arise in problems in analysis, in particular complex analysis and harmonic analysis. The two main singular integral operators, the Hilbert transform and the Cauchy transform, can be defined for any smooth Jordan curve in the complex plane and are related by a simple algebraic formula. The Hilbert transform is an involution and the Cauchy transform an idempotent. The range of the Cauchy transform is the Hardy space of the bounded region enclosed by the Jordan curve. The theory for the original curve can be deduced from that on the unit circle, where, because of rotational symmetry, both operators are classical singular integral operators of convolution type. The Hilbert transform satisfies the jump relations of Plemelj and Sokhotski, which express the original function as the difference between the boundary values of holomorphic functions on the region and its complement. Singular integral operators have been studied on various classes of functions, including Hőlder spaces, Lp spaces and Sobolev spaces. In the case of L2 spaces—the case treated in detail below—other operators associated with the closed curve, such as the Szegő projection onto Hardy space and the Neumann–Poincaré operator, can be expressed in terms of the Cauchy transform and its adjoint.".
- Singular_integral_operators_on_closed_curves wikiPageID "36924582".
- Singular_integral_operators_on_closed_curves wikiPageRevisionID "577000363".
- Singular_integral_operators_on_closed_curves hasPhotoCollection Singular_integral_operators_on_closed_curves.
- Singular_integral_operators_on_closed_curves subject Category:Complex_analysis.
- Singular_integral_operators_on_closed_curves subject Category:Harmonic_analysis.
- Singular_integral_operators_on_closed_curves subject Category:Operator_theory.
- Singular_integral_operators_on_closed_curves comment "In mathematics, singular integral operators on closed curves arise in problems in analysis, in particular complex analysis and harmonic analysis. The two main singular integral operators, the Hilbert transform and the Cauchy transform, can be defined for any smooth Jordan curve in the complex plane and are related by a simple algebraic formula. The Hilbert transform is an involution and the Cauchy transform an idempotent.".
- Singular_integral_operators_on_closed_curves label "Singular integral operators on closed curves".
- Singular_integral_operators_on_closed_curves sameAs m.0m0kfxv.
- Singular_integral_operators_on_closed_curves sameAs Q7524243.
- Singular_integral_operators_on_closed_curves sameAs Q7524243.
- Singular_integral_operators_on_closed_curves wasDerivedFrom Singular_integral_operators_on_closed_curves?oldid=577000363.
- Singular_integral_operators_on_closed_curves isPrimaryTopicOf Singular_integral_operators_on_closed_curves.