Spectral Mapping Theorem for the Davies-Helffer-Sjöstrand Functional Calculus
We give a direct non-abstract proof of the spectral mapping theorem for the Davies–Helffer–Sjöstrand functional calculus for linear operators on Banach spaces with real spectra and consequently give a new non-abstract direct proof for the spectral mapping theorem for self-adjoint operators on Hilber...
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| Datum: | 2012 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2012
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| Schriftenreihe: | Журнал математической физики, анализа, геометрии |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/106720 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Spectral Mapping Theorem for the Davies-Helffer-Sjöstrand Functional Calculus / N.S. Claire // Журнал математической физики, анализа, геометрии. — 2012. — Т. 8, № 3. — С. 221-239. — Бібліогр.: 8 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We give a direct non-abstract proof of the spectral mapping theorem for the Davies–Helffer–Sjöstrand functional calculus for linear operators on Banach spaces with real spectra and consequently give a new non-abstract direct proof for the spectral mapping theorem for self-adjoint operators on Hilbert spaces. Our exposition is closer in spirit to the proof by explicit construction of the existence of the Functional Calculus given by Davies. We apply an extension theorem of Seeley to derive a functional calculus for semi-bounded operators. |
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