{"product_id":"9783034899048","title":"The Bochner-Martinelli Integral and Its Applications","description":"\u003ch1\u003eThe Bochner-Martinelli Integral and Its Applications\u003c\/h1\u003e \u003ch2\u003eKytmanov, Alexander M.\u003c\/h2\u003e \u003cp\u003eThe 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 \u0026gt; 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 \u0026gt; 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 single-layer potential. Therefore the Bochner-Martinelli integral has a jump that agrees with the integrand, but it behaves like the Cauchy integral under approach to the boundary, that is, somewhat worse than the double-layer potential. Thus, the Bochner-Martinelli integral combines properties of the Cauchy integral and the double-layer potential.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Birkhäuser\u003c\/p\u003e \u003cp\u003ePublication Date: 2011-10-08\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783034899048\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-0348-9094-6\u003c\/p\u003e \u003cp\u003eDimensions: 244cm x170cm\u003c\/p\u003e \u003cp\u003ePages: 308\u003c\/p\u003e ","brand":"Birkhäuser Basel","offers":[{"title":"Default Title","offer_id":44340577599628,"sku":"9783034899048","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783034899048.jpg?v=1775793586","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783034899048","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}