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| Hlavní autor: | |
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| Médium: | Preprint |
| Vydáno: |
2026
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| Témata: | |
| On-line přístup: | https://arxiv.org/abs/2602.04424 |
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Obsah:
- 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.