Abstract:We analyze the parabolic Dirac operator $D \pm i\partial_t$ in a biquaternionic setting, characterizing its kernel via generalized div-curl systems and Cauchy-Riemann-type relations between the real and imaginary parts. Using the machinery provided by the Fourier transform, we fully characterize the Fourier transform of a fundamental solution of this operator and construct a well-defined right inverse operator. As an application, we derive explicit vectorial solutions to the time-dependent Maxwell system, extending prior biquaternionic approaches. These tools offer analytical efficiency for complex electromagnetic problems.
| Subjects: | Analysis of PDEs (math.AP) |
| MSC classes: | 42A38, 47S02, 35Q61, 30G35 |
| Cite as: | arXiv:2605.21412 [math.AP] |
| (or arXiv:2605.21412v2 [math.AP] for this version) | |
| https://doi.org/10.48550/arXiv.2605.21412 arXiv-issued DOI via DataCite |
From: Briceyda B. Delgado [view email]
[v1]
Wed, 20 May 2026 17:08:36 UTC (17 KB)
[v2]
Fri, 22 May 2026 17:58:33 UTC (17 KB)
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