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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2012
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1207.1730 |
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| _version_ | 1866916435555516416 |
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| author | Alvarez-Peña, Cynthia Porter, R. Michael |
| author_facet | Alvarez-Peña, Cynthia Porter, R. Michael |
| contents | It is shown that harmonic functions from a simply connected domain in R^3 to R^3 cannot always be expressed as a sum of a monogenic (hyperholomorphic) function and an antimonogenic function, in contrast to the situation for complex numbers or quaternions. Harmonic functions orthogonal in L_2 to all such sums are termed "contragenic" and their properties are studied. A "Bergman kernel" and is derived, whose corresponding operator vanishes precisely on the contragenic functions. A graded orthonormal basis for the contragenic function in the ball B^3 is given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1207_1730 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | Contragenic Functions of Three Variables Alvarez-Peña, Cynthia Porter, R. Michael Complex Variables It is shown that harmonic functions from a simply connected domain in R^3 to R^3 cannot always be expressed as a sum of a monogenic (hyperholomorphic) function and an antimonogenic function, in contrast to the situation for complex numbers or quaternions. Harmonic functions orthogonal in L_2 to all such sums are termed "contragenic" and their properties are studied. A "Bergman kernel" and is derived, whose corresponding operator vanishes precisely on the contragenic functions. A graded orthonormal basis for the contragenic function in the ball B^3 is given. |
| title | Contragenic Functions of Three Variables |
| topic | Complex Variables |
| url | https://arxiv.org/abs/1207.1730 |