×

Unbounded, symmetric semigroups on a separable Hilbert space are essentially selfadjoint. (English) Zbl 0452.47043


MSC:

47D03 Groups and semigroups of linear operators
47B25 Linear symmetric and selfadjoint operators (unbounded)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Fröhlich, J., Ann. Phys. (N.Y.), 97, 1 (1976)
[2] Driessler, W.; Fröhlich, J., Ann. Inst. H. Poincaré, Sect. A, 27, 221 (1977)
[3] E. B. Davies; E. B. Davies
[4] Ruelle, D., Helv. Phys. Acta, 45, 215 (1972)
[5] J. Frölich; J. Frölich
[6] Osterwalder, K.; Schrader, R., Commun. Math. Phys., 42, 281 (1975)
[7] Glaser, V., Commun. Math. Phys., 37, 257 (1974)
[8] Fröhlich, J., Helv. Phys. Acta, 48, 355 (1975)
[9] Klein, A.; Landau, L. J., Construction of a unique selfadjoint generator for a symmetric local semigroup, preprint (1979)
[10] Klein, A.; Landau, L. J., Stochastic processes associated with KMS states, preprint (1980)
[11] Glaser, V., (Problems of theoretical physics (1969), Nauka: Nauka Moscow), 69
[12] Fröhlich, J., (Lévy, M.; Mitter, P., Cargèse Lectures (1979)), to appear
[13] Achieser, N. I.; Glasmann, I. M., Theorie der linearen Operatoren im Hisbert Raum (1968), Akademie-Verlag: Akademie-Verlag Berlin · Zbl 0056.11101
[14] Nelson, E., Ann. Math., 70, 572 (1959)
[15] Reed, M.; Simon, B., Methods of Modern Mathematical Physics (1975), Academic Press: Academic Press New York, Chap. X.6
[16] Reed, M.; Simon, B., Methods of Modern Mathematical Physics (1975), Academic Press: Academic Press New York, Chap. X.5
[17] Sokal, A., An improvement of Watson’s theorem on Borel summability, preprint (1979)
[18] Nevanlinna, F., Ann. Acad. Sci. Fermicae, Ser. A, 12, No. 3 (1918-1919)
[19] Gel’fand, I. M.; Vilenkin, N. Ya, (Generalized Functions, Vol. 4 (1964), Academic Press: Academic Press New York/London), For related results, see also
[20] Simon, B., Functional Integration and Quantum Physics (1979), Academic Press: Academic Press New York · Zbl 0434.28013
[21] Avron, Y.; Herbst, I., Commun. Math. Phys., 52, 239 (1977)
[22] Faris, W.; Lavine, R., Commun. Math. Phys., 35, 39 (1974)
[23] Davies, E. B.; Simon, B., Commun. Math. Phys., 63, 277 (1978)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.