Some properties of singular integral operators over an open curve |
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Authors: | Yong-jia Xu |
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Affiliation: | (1) Guangdong University of Business Studies, Guangzhou, 510320, China |
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Abstract: | In this paper, the stability properties, the endpoint behavior and the invertible relations of Cauchy-type singular integral
operators over an open curve are discussed. If the endpoints of the curve are not special, this type of operators are proved
to be stable. At the endpoints, either the singularity or smoothness of the operators are exactly described. And the function
sets or spaces on which the operators are invertible as well as the corresponding inverted operators are given. Meanwhile,
some applications for the solution of Cauchy-type singular integral equations are illustrated.
This work was partially supported by the National Natural Science Foundation of China (Grant No. 10471048) |
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Keywords: | stability endpoint behavior singular integral operator paired operators |
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