caa a22 4500 47707538X CHVBK 20180405111438.0 cr unu---uuuuu 170330e19960601xx s 000 0 eng 10.1007/BF02901217 doi (NATIONALLICENCE)springer-10.1007/BF02901217 On convergence of singular integral operators with respect to path of integration [Elektronische Daten] [Wang Xiaolin, Lu Jianke] Givenf being Hölder continuous in a regionG⊂C. For the Cauchy principal integral $$I(\Gamma ,f) = \frac{1}{{\pi i}} \int_\Gamma {\frac{{f(\zeta )}}{{\zeta - \zeta _0 }}d\zeta , \zeta _0 \in \Gamma } $$ where Γ⊂G is a smooth closed contour, it is established that, if a sequence of smooth closed contours Γn⊂G(n∈N) smoothly convergent to Γ, then the corresponding sequenceI(Γ n, f)is convergent to I(Γ, f). Furthermore, when Γ is approximated by a sequence of complex cubic splines $$S_{\Delta _n } (\Gamma )$$ interpolatory to Γ, the error $$|I(\Gamma ,f)--I(S_{\Delta _n } (\Gamma ,f)|$$ is estimated. Springer, 1996 singular integral operator nationallicence smooth convergence nationallicence complex interpolatory spline nationallicence Xiaolin Wang Department of Mathematics, Wuhan University, 430072, Wuhan, China aut Jianke Lu Department of Mathematics, Wuhan University, 430072, Wuhan, China aut Wuhan University Journal of Natural Sciences Wuhan University 1/2(1996-06-01), 144-148 1007-1202 1:2<144 1996 1 11859 https://doi.org/10.1007/BF02901217 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02901217 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Xiaolin Wang Department of Mathematics, Wuhan University, 430072, Wuhan, China aut NATIONALLICENCE 700 1- Jianke Lu Department of Mathematics, Wuhan University, 430072, Wuhan, China aut NATIONALLICENCE 773 0- Wuhan University Journal of Natural Sciences Wuhan University 1/2(1996-06-01), 144-148 1007-1202 1:2<144 1996 1 11859 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer