The finite part of singular integrals in several complex variables
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- by Xiaoqin Wang PDF
- Trans. Amer. Math. Soc. 337 (1993), 771-793 Request permission
Abstract:
A divergent integral can sometimes be handled by assigning to it as its value the finite part in the sense of Hadamard. This is done by expanding the integral over the complement of a symmetric neighborhood of a singularity in powers of the radius, and throwing away the negative powers. In this paper the finite part of a singular integral of Cauchy type is defined, and this is then used to describe the boundary behavior of derivatives of a Cauchy-type integral. The finite part of a singular integral of Bochner-Martinelli type is studied, and an extension of the Plemelj jump formulas is shown to hold.References
- Charles Fox, A generalization of the Cauchy principal value, Canadian J. Math. 9 (1957), 110–117. MR 92037, DOI 10.4153/CJM-1957-015-1
- Sheng Gong, Duo fu bianshu de qiyi jifen, Xiandai Shuxue Congshu. [Modern Mathematics Series], Shanghai Kexue Jishu Chubanshe, Shanghai, 1982 (Chinese). With an English summary. MR 898221 Hadamard, Lectures on Cauchy’s problem in linear partial differential equations, Dover, New York, 1952.
- Lars Hörmander, The analysis of linear partial differential operators. I, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 256, Springer-Verlag, Berlin, 1983. Distribution theory and Fourier analysis. MR 717035, DOI 10.1007/978-3-642-96750-4 Qi-keng Lu and Tongde Zhong, A generalization of Privalov’s theorem, Chinese Math. 7 (1957), 144-165. (Chinese)
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 337 (1993), 771-793
- MSC: Primary 32A25
- DOI: https://doi.org/10.1090/S0002-9947-1993-1120777-0
- MathSciNet review: 1120777