Constructing steering-type solutions for higher order Cauchy-Riemann equations in $\mathbb{R}^{m+1}$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912773548539904 |
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| author | Santiesteban, Daniel Alfonso Peña, Dixan Peña Blaya, Ricardo Abreu |
| author_facet | Santiesteban, Daniel Alfonso Peña, Dixan Peña Blaya, Ricardo Abreu |
| contents | The multidimensional Cauchy-Riemann operator provides a framework for studying higher order partial differential equations in $\mathbb{R}^{m+1}$, whose solutions include polymonogenic and polyharmonic functions, among others. In this work, we aim to explicitly construct solutions to such systems, generated from families of complex valued functions which are closed under conjugation and under the action of the complex Cauchy-Riemann operator. Moreover, we prove that precisely some of these solutions also satisfy homogeneous linear differential equations involving the so-called hypercomplex derivative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16594 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constructing steering-type solutions for higher order Cauchy-Riemann equations in $\mathbb{R}^{m+1}$ Santiesteban, Daniel Alfonso Peña, Dixan Peña Blaya, Ricardo Abreu Analysis of PDEs Mathematical Physics 30G35, 30G30, 35J15, 35J25, 35J47, 35J57 The multidimensional Cauchy-Riemann operator provides a framework for studying higher order partial differential equations in $\mathbb{R}^{m+1}$, whose solutions include polymonogenic and polyharmonic functions, among others. In this work, we aim to explicitly construct solutions to such systems, generated from families of complex valued functions which are closed under conjugation and under the action of the complex Cauchy-Riemann operator. Moreover, we prove that precisely some of these solutions also satisfy homogeneous linear differential equations involving the so-called hypercomplex derivative. |
| title | Constructing steering-type solutions for higher order Cauchy-Riemann equations in $\mathbb{R}^{m+1}$ |
| topic | Analysis of PDEs Mathematical Physics 30G35, 30G30, 35J15, 35J25, 35J47, 35J57 |
| url | https://arxiv.org/abs/2512.16594 |