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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 wikiPageLength "28580".
- Singular_integral_operators_on_closed_curves wikiPageOutDegree "37".
- Singular_integral_operators_on_closed_curves wikiPageRevisionID "696158167".
- Singular_integral_operators_on_closed_curves wikiPageWikiLink American_Mathematical_Society.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Analysis.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Bergman_space.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Carathéodory_kernel_theorem.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Category:Complex_analysis.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Category:Harmonic_analysis.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Category:Operator_theory.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Cauchy_principal_value.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Cauchy_transform.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Cauchys_integral_formula.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Complex_analysis.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Curvature.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Graduate_Studies_in_Mathematics.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Greens_theorem.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Hardy_space.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Harmonic_analysis.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Hartogs–Rosenthal_theorem.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Hilbert_transform.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Hilbert–Schmidt_operator.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Hölder_condition.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Idempotence.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Involution_(mathematics).
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Jean_Frédéric_Frenet.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Joseph_L._Walsh.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Mathematics.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Mergelyans_theorem.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Methods_of_contour_integration.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Neumann–Poincaré_operator.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Operator_norm.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Singular_integral_operators_of_convolution_type.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Sokhotski–Plemelj_theorem.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Strong_operator_topology.
- Singular_integral_operators_on_closed_curves wikiPageWikiLink Szegő_kernel.
- Singular_integral_operators_on_closed_curves wikiPageWikiLinkText "Hilbert transform".
- Singular_integral_operators_on_closed_curves wikiPageWikiLinkText "Singular integral operators on closed curves".
- Singular_integral_operators_on_closed_curves wikiPageUsesTemplate Template:Citation.
- Singular_integral_operators_on_closed_curves wikiPageUsesTemplate Template:Harvtxt.
- Singular_integral_operators_on_closed_curves wikiPageUsesTemplate Template:Main.
- Singular_integral_operators_on_closed_curves wikiPageUsesTemplate Template:Reflist.
- Singular_integral_operators_on_closed_curves wikiPageUsesTemplate Template:See_also.
- 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 type Physic.
- Singular_integral_operators_on_closed_curves type Thing.
- 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 seeAlso Hardy_space.
- Singular_integral_operators_on_closed_curves seeAlso Sokhotski–Plemelj_theorem.
- Singular_integral_operators_on_closed_curves seeAlso Szegő_kernel.
- Singular_integral_operators_on_closed_curves sameAs Q7524243.
- Singular_integral_operators_on_closed_curves sameAs m.0m0kfxv.
- Singular_integral_operators_on_closed_curves sameAs Q7524243.
- Singular_integral_operators_on_closed_curves wasDerivedFrom Singular_integral_operators_on_closed_curves?oldid=696158167.
- Singular_integral_operators_on_closed_curves isPrimaryTopicOf Singular_integral_operators_on_closed_curves.