Selfadjoint operator extensions satisfying the Weyl commutation relations
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- by Palle E. T. Jørgensen PDF
- Bull. Amer. Math. Soc. 1 (1979), 266-269
References
- C. Foiaş and L. Gehér, Über die Weylsche Vertauschungsrelation, Acta Sci. Math. (Szeged) 24 (1963), 97–102 (German). 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).
- M. A. Naĭmark, On commuting unitary operators in spaces with indefinite metric, Acta Sci. Math. (Szeged) 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.
- Neils Skovhus Poulsen, On $C^{\infty }$-vectors and intertwining bilinear forms for representations of Lie groups, J. Functional Analysis 9 (1972), 87–120. MR 0310137, DOI 10.1016/0022-1236(72)90016-x
- Robert T. Powers, Selfadjoint algebras of unbounded operators. II, Trans. Amer. Math. Soc. 187 (1974), 261–293. MR 333743, DOI 10.1090/S0002-9947-1974-0333743-8
- R. Ranga Rao, Unitary representations defined by boundary conditions—the case of ${\mathfrak {s}}{\mathfrak {l}}(2, \textbf {R})$, Acta Math. 139 (1977), no. 3-4, 185–216. MR 507246, DOI 10.1007/BF02392237
- Donald Sarason, On spectral sets having connected complement, Acta Sci. Math. (Szeged) 26 (1965), 289–299. MR 188797
- Irving Segal, Nonlinear functions of weak processes. II, J. Functional Analysis 6 (1970), 29–75. MR 0263369, DOI 10.1016/0022-1236(70)90046-7 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.
- Peter D. Lax and Ralph S. Phillips, Scattering theory, Pure and Applied Mathematics, Vol. 26, Academic Press, New York-London, 1967. MR 0217440
Additional Information
- Journal: Bull. Amer. Math. Soc. 1 (1979), 266-269
- MSC (1970): Primary 47B25, 81A20; Secondary 43A65, 46K99, 47B47
- DOI: https://doi.org/10.1090/S0273-0979-1979-14583-X
- MathSciNet review: 513756