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Item Details
| Title:
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THE BOCHNER-MARTINELLI INTEGRAL AND ITS APPLICATIONS
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| By: |
Alexander M. Kytmanov |
| Format: |
Paperback |
| List price:
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£79.99 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
3034899041 |
| ISBN 13: |
9783034899048 |
| Publisher: |
SPRINGER BASEL |
| Pub. date: |
8 October, 2011 |
| Edition: |
Softcover reprint of the original 1st ed. 1995 |
| Pages: |
308 |
| Synopsis: |
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 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. |
| Illustrations: |
biography |
| Publication: |
Switzerland |
| Imprint: |
Springer Basel |
| Returns: |
Returnable |
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Ramadan and Eid al-Fitr
A celebratory, inclusive and educational exploration of Ramadan and Eid al-Fitr for both children that celebrate and children who want to understand and appreciate their peers who do.
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