Duke Mathematical Journal

A new proof of the Mourre estimate

Richard Froese and Ira Herbst
Source: Duke Math. J. Volume 49, Number 4 (1982), 1075-1085.
First Page: Show Hide
Primary Subjects: 35P99
Secondary Subjects: 47F05, 81C10
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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077315539
Mathematical Reviews number (MathSciNet): MR683011
Zentralblatt MATH identifier: 0514.35025
Digital Object Identifier: doi:10.1215/S0012-7094-82-04947-X

References

[1] S. Agmon, Lectures on exponential decay of solutions of second order elliptic equations, Bounds on eigenfunctions of $N$-body Schrödinger operators, to be published.
[2] V. Enss, A note on Hunziker's theorem, Comm. Math. Phys. 52 (1977), no. 3, 233–238.
Mathematical Reviews (MathSciNet): MR56:4524
Digital Object Identifier: doi:10.1007/BF01609484
Project Euclid: euclid.cmp/1103900537
[3] R. Froese and I. Herbst, Exponential bounds and absence of positive eigenvalues for $N$-body Schrödinger operators, to appear in Commun. Math. Phys.
Mathematical Reviews (MathSciNet): MR682117
Digital Object Identifier: doi:10.1007/BF01206033
Project Euclid: euclid.cmp/1103922052
[4] H. Kalf, The quantum mechanical virial theorem and the absence of positive energy bound states of Schrödinger operators, Israel J. Math. 20 (1975), 57–69.
Mathematical Reviews (MathSciNet): MR51:8647
Zentralblatt MATH: 0302.35072
Digital Object Identifier: doi:10.1007/BF02756756
[5] E. Mourre, Absence of singular continuous spectrum for certain selfadjoint operators, Comm. Math. Phys. 78 (1980/81), no. 3, 391–408.
Mathematical Reviews (MathSciNet): MR82c:47030
Zentralblatt MATH: 0489.47010
Digital Object Identifier: doi:10.1007/BF01942331
Project Euclid: euclid.cmp/1103908694
[6] P. Perry, I. M. Sigal, and B. Simon, Spectral analysis of $N$-body Schrödinger operators, Ann. of Math. (2) 114 (1981), no. 3, 519–567.
Mathematical Reviews (MathSciNet): MR83b:81129
Zentralblatt MATH: 0477.35069
Digital Object Identifier: doi:10.2307/1971301
[7] I. M. Sigal, Geometric methods in the quantum many-body problem. Nonexistence of very negative ions, Comm. Math. Phys. 85 (1982), no. 2, 309–324.
Mathematical Reviews (MathSciNet): MR83m:81117
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[8] B. Simon, Geometric methods in multiparticle quantum systems, Comm. Math. Phys. 55 (1977), no. 3, 259–274.
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Project Euclid: euclid.cmp/1103901023
[9] B. Simon, personal communication.
[10] J. Weidmann, The virial theorem and its application to the spectral theory of Schrödinger operators, Bull. Amer. Math. Soc. 73 (1967), 452–456.
Mathematical Reviews (MathSciNet): MR34:8007
Zentralblatt MATH: 0156.23304
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[11] G. M. Zhislin, Discussion of the spectrum of the Schrödinger operator for systems of many particles, Tr. Mosk. Mat. Obs. 9 (1960), 81–128.
Zentralblatt MATH: 0121.10004

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