The $H^\infty$-functional calculi for the quaternionic fine structures of Dirac type
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914688998047744 |
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| author | Colombo, Fabrizio Pinton, Stefano Schlosser, Peter |
| author_facet | Colombo, Fabrizio Pinton, Stefano Schlosser, Peter |
| contents | In this paper, we utilize various integral representations derived from the Fueter-Sce extension theorem, to introduce novel functional calculi tailored for quaternionic operators of sectorial type. Specifically, due to the different factorizations of the Laplace opertor with respect to the Cauchy-Fueter operator and its conjugate, we identify four distinct classes of functions: Slice hyperholomorphic functions (leading to the $S$-functional calculus), axially harmonic functions (leading to the $Q$-functional calculus), axially polyanalytic functions of order $2$ (leading to the $P_2$-functional calculus), and axially monogenic functions (leading to the $F$-functional calculus). By applying the respective product rule, we establish the four different $H^\infty$-versions of these functional calculi. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_02064 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The $H^\infty$-functional calculi for the quaternionic fine structures of Dirac type Colombo, Fabrizio Pinton, Stefano Schlosser, Peter Functional Analysis In this paper, we utilize various integral representations derived from the Fueter-Sce extension theorem, to introduce novel functional calculi tailored for quaternionic operators of sectorial type. Specifically, due to the different factorizations of the Laplace opertor with respect to the Cauchy-Fueter operator and its conjugate, we identify four distinct classes of functions: Slice hyperholomorphic functions (leading to the $S$-functional calculus), axially harmonic functions (leading to the $Q$-functional calculus), axially polyanalytic functions of order $2$ (leading to the $P_2$-functional calculus), and axially monogenic functions (leading to the $F$-functional calculus). By applying the respective product rule, we establish the four different $H^\infty$-versions of these functional calculi. |
| title | The $H^\infty$-functional calculi for the quaternionic fine structures of Dirac type |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2312.02064 |