Spectral representation of local symmetric semigroups of operators over topological groups
We consider local symmetric semigroups of Hilbert space operators. For an open semigroup & in some topological group and a dense subsemigroup 6' of 6, these are semigroups of unbounded selfadjoint operators (ii(i))t e s' that admit local continuous extensions to open subsets of 6. We s...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2012
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| Sorozat: | Acta scientiarum mathematicarum
78 No. 1-2 |
| Kulcsszavak: | Matematika, Operátorelmélet |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16434 |
| Tartalmi kivonat: | We consider local symmetric semigroups of Hilbert space operators. For an open semigroup & in some topological group and a dense subsemigroup 6' of 6, these are semigroups of unbounded selfadjoint operators (ii(i))t e s' that admit local continuous extensions to open subsets of 6. We study the possibility to continuously extend H(-) to a semigroup of selfadjoint operators defined for all t G 6 in several settings. Integral representation formulae for the extended semigroups (H(t))teQ by means of real characters of 6 are established. Our proofs rely on graph limits of selfadjoint operators, commutativity of unbounded operators and semigroup techniques, among others. |
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| Terjedelem/Fizikai jellemzők: | 291-314 |
| ISSN: | 0001-6969 |