| 書目名稱 | The Bochner-Martinelli Integral and Its Applications | | 編輯 | Alexander M. Kytmanov | | 視頻video | http://file.papertrans.cn/906/905312/905312.mp4 | | 圖書封面 |  | | 描述 | The Bochner-Martinelli integral representation for holomorphic functions or‘sev- eral complex variables (which has already become classical) appeared in the works of Martinelli and Bochner at the beginning of the 1940‘s. It was the first essen- tially multidimensional representation in which the integration takes place over the whole boundary of the domain. This integral representation has a universal 1 kernel (not depending on the form of the domain), like the Cauchy kernel in e . However, in en when n > 1, the Bochner-Martinelli kernel is harmonic, but not holomorphic. For a long time, this circumstance prevented the wide application of the Bochner-Martinelli integral in multidimensional complex analysis. Martinelli and Bochner used their representation to prove the theorem of Hartogs (Osgood- Brown) on removability of compact singularities of holomorphic functions in en when n > 1. In the 1950‘s and 1960‘s, only isolated works appeared that studied the boundary behavior of Bochner-Martinelli (type) integrals by analogy with Cauchy (type) integrals. This study was based on the Bochner-Martinelli integral being the sum of a double-layer potential and the tangential derivative of a | | 出版日期 | Book 1995 | | 關(guān)鍵詞 | Complex analysis; derivative; holomorphic function; integral; integration | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-0348-9094-6 | | isbn_softcover | 978-3-0348-9904-8 | | isbn_ebook | 978-3-0348-9094-6 | | copyright | Birkh?user Verlag 1995 |
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