Slice hyperholomorphicity of the $S$-resolvent operators and boundary conditions
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910011542732800 |
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| author | Mantovani, Francesco |
| author_facet | Mantovani, Francesco |
| contents | The foundation of spectral theory on the $S$-spectrum can be traced back to the quaternionic framework of quantum mechanics. The concept of $S$-spectrum for quaternionic operators emerged as the natural spectrum in slice hyperholomorphic functional calculi, known as the $S$-functional calculus and also utilized in the quaternionic spectral theorem. This spectral theory extends to Clifford operators. A key distinction from classical complex spectral theory lies in the definition of the $S$-spectrum, which is second order in the operator $T$, and in the $S$-resolvent operators that turns out to be the product of two different operators. This study delves into the analyticity of the $S$-resolvent operators under specified boundary conditions for the $S$-spectral problem. The spectral theory on the $S$-spectrum also provides deeper insights into classical spectral theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_04424 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Slice hyperholomorphicity of the $S$-resolvent operators and boundary conditions Mantovani, Francesco Spectral Theory Functional Analysis The foundation of spectral theory on the $S$-spectrum can be traced back to the quaternionic framework of quantum mechanics. The concept of $S$-spectrum for quaternionic operators emerged as the natural spectrum in slice hyperholomorphic functional calculi, known as the $S$-functional calculus and also utilized in the quaternionic spectral theorem. This spectral theory extends to Clifford operators. A key distinction from classical complex spectral theory lies in the definition of the $S$-spectrum, which is second order in the operator $T$, and in the $S$-resolvent operators that turns out to be the product of two different operators. This study delves into the analyticity of the $S$-resolvent operators under specified boundary conditions for the $S$-spectral problem. The spectral theory on the $S$-spectrum also provides deeper insights into classical spectral theory. |
| title | Slice hyperholomorphicity of the $S$-resolvent operators and boundary conditions |
| topic | Spectral Theory Functional Analysis |
| url | https://arxiv.org/abs/2602.04424 |