Leutwiler H (2024)
Publication Type: Journal article
Publication year: 2024
Book Volume: 47
Pages Range: 7879-7887
Journal Issue: 10
DOI: 10.1002/mma.7277
The Weinstein equation (Formula presented.), with (Formula presented.), considered in (Formula presented.), is a modification of the classical Laplace equation (Formula presented.). Its solutions are called k-modified harmonic functions. Whereas for positive integers k the Weinstein equation is relatively well understood, little is known if the parameter k is negative. The main result of this article is the statement that in case the negative integers are even, i.e., (Formula presented.), we still have a Fischer-type decomposition. For (Formula presented.), the classical harmonic functions, this decomposition is well known. But also in case (Formula presented.), a Fischer-type decomposition holds true, a Fischer-type decomposition holds true. Surprisingly in case (Formula presented.) or (Formula presented.) and probably in all higher negative odd cases, the decomposition doesn't hold. In case (Formula presented.), we give a complete description of the vector space (Formula presented.) of homogeneous k-modified harmonic polynomials of degree n in (Formula presented.). Such a result is also at hand in case (Formula presented.). Finally, in case (Formula presented.) of the classical harmonic functions, we give a description of the vector space (Formula presented.).
APA:
Leutwiler, H. (2024). Further results on modified harmonic functions in three dimensions. Mathematical Methods in the Applied Sciences, 47(10), 7879-7887. https://doi.org/10.1002/mma.7277
MLA:
Leutwiler, Heinz. "Further results on modified harmonic functions in three dimensions." Mathematical Methods in the Applied Sciences 47.10 (2024): 7879-7887.
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