Special bases for solutions of a generalized Maxwell system in 3‐dimensional space
The aim of this paper is to study complete polynomial systems in the kernel space of conformally invariant differential operators in higher spin theory. We investigate the kernel space of a generalized Maxwell operator in 3‐dimensional space. With the already known decomposition of its homogeneous k...
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Published in: | Mathematical methods in the applied sciences Vol. 41; no. 13; pp. 5308 - 5326 |
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Main Authors: | , , |
Format: | Journal Article |
Language: | English |
Published: |
Freiburg
Wiley Subscription Services, Inc
15-09-2018
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Subjects: | |
Online Access: | Get full text |
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Summary: | The aim of this paper is to study complete polynomial systems in the kernel space of conformally invariant differential operators in higher spin theory. We investigate the kernel space of a generalized Maxwell operator in 3‐dimensional space. With the already known decomposition of its homogeneous kernel space into 2 subspaces, we investigate first projections from the homogeneous kernel space to each subspace. Then, we provide complete polynomial systems depending on the given inner product for each subspace in the decomposition. More specifically, the complete polynomial system for the homogenous kernel space is an orthogonal system wrt a given Fischer inner product. In the case of the standard inner product in L2 on the unit ball, the provided complete polynomial system for the homogeneous kernel space is a partially orthogonal system. Further, if the degree of homogeneity for the respective subspaces in the decomposed kernel spaces approaches infinity, then the angle between the 2 subspaces approaches π/2. |
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ISSN: | 0170-4214 1099-1476 |
DOI: | 10.1002/mma.5081 |