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Selfadjoint operator extensions satisfying the Weyl commutation relations
Author(s):
Palle E. T.
Jørgensen
Journal:
Bull. Amer. Math. Soc.
1
(1979),
266-269.
MSC (1970):
Primary 47B25, 81A20;
Secondary 43A65, 46K99, 47B47
MathSciNet review:
513756
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Additional information
References:
- 1.
- C. Foiaş and L. Gehér, Über die Weylsche Vertauschungsrelationen, Acta Sci Math. 24 (1963), 97-102. MR 150601
- 2.
- P. E. T. Jørgensen (a) (with R. T. Moore), Commutation relations for operators, semigroups, and resolvents in mathematical physics and group representations (preprint); P. E. T. Jørgensen, (b) (with P. S. Muhly), Selfadjoint extensions satisfying the Weyl operator commutation relations (in preparation).
- 3.
- M. A. Naĭmark, On commuting unitary operators in spaces with indefinite metric. Acta Sci. Math. 24 (1963), 177-189. MR 161158
- 4.
- J. von Neumann, (a) Allgemeine Eigenwerttheorie Hermitescher Funktionaloperatoren. Math. Ann. 102 (1929-30) 49-131; J. von Neumann, (b) Die Eindentigkeit der Schrödingerschen Operatoren, Math. Ann. 104 (1931), 570-578.
- 5.
- R. S. Phillips, On dissipative operators, Lecture Series in Differential Equations, vol. II. A. K. Aziz (Ed.), Van Nostrand Mathematical Studies no. 19, Van Nostrand, New York, 1969.
- 6.
- N. S. Poulsen, On C, J. Functional Analysis, (1972), 87-120. MR 310137
- 7.
- R. T. Powers, On selfadjoint algebras of unbounded operators, Trans. Amer. Math. Soc 187 (1974), 261-293. MR 333743
- 8.
- R. R. Rao, Unitary representations defined by boundary conditions-the case of sl (2, R), Acta Math. 139 (1977), 185-216, MR 507246
- 9.
- D. Sarason, On spectral sets having connected complement, Acta Sci. Math, 26 (1965), 289-299. MR 188797
- 10.
- L E. Segal, Nonlinear functions of weak processes, II, J, Functional Analysis 6 (1970), 29-75. MR 263369
- 11.
- I. M. Singer, Lie algebras of unbounded operators, Thesis, Univ. of Chicago, 1950.
- 12.
- M. H. Stone, Linear transformations in Hubert space. III. Operational methods and group theory, Proc. Nat. Acad. Sci. U.S.A. 16 (1930), 172-175.
- [LP] P. D. Lax and R. S, Phillips, Scattering theory, Academic Press, New York, 1967. MR 217440
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Additional Information:
DOI:
10.1090/S0273-0979-1979-14583-X
PII:
S 0273-0979(1979)14583-X
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