Variations on a Theme by Mikhlin

Joseph Nieto

A chapter in Contributions to Functional Analysis, 1966, pp 331-336 from Springer

Abstract: Abstract In [5] Mikhlin develops the L 2 theory of singular integral operators on a simple closed plane curve Γ of class C 2. His main results are: (a) The operator H, defined by % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qacaGGOaGaamisa8aacaaMh8+dbiabeA8aQjaacMcapaGaaG5bV-qa % caGGOaGaamOEaiaacMcapaGaaG5bV-qacqGH9aqppaGaaG5bV-qada % WcaaWdaeaapeGaaGymaaWdaeaapeGaeqiWdaNaamyAaaaadaWdrbWd % aeaapeWaaSaaa8aabaWdbiabeA8aQjaacIcacqaH2oGEcaGGPaaapa % qaa8qacqaH2oGEpaGaaG5bV-qacqGHsislpaGaaG5bV-qacaWG6baa % aiaadsgacqaH2oGEcaGGSaWdaiaayEW7peGaamOEa8aacaaMh8+dbi % abgIGio-aacaaMh8+dbiabfo5ahbWcpaqaa8qacqqHtoWraeqaniab % gUIiYdaaaa!642B! $$(H{\mkern 1mu} \varphi ){\mkern 1mu} (z){\mkern 1mu} = {\mkern 1mu} \frac{1}{{\pi i}}\int\limits_\Gamma {\frac{{\varphi (\zeta )}}{{\zeta {\mkern 1mu} - {\mkern 1mu} z}}d\zeta ,{\mkern 1mu} z{\mkern 1mu} \in {\mkern 1mu} \Gamma } $$ is a linear bounded operator from L 2(Γ) into L 2(Γ).

Keywords: Banach Space; Compact Operator; Elliptic Operator; Compact Manifold; Closed Operator (search for similar items in EconPapers)
Date: 1966
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DOI: 10.1007/978-3-642-85997-7_21

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