The essential spectrum of relativistic multi-particle operators

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1. [1] S. Agmon, Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations: Bounds on Eigenfunctions of N-body Schrödinger Operators. Mathematical Notes 29. Princeton University Press, Princeton, 1 edition, 1982. Zbl0503.35001MR745286
2. [2] E Balslev, Schrödinger operators with symmetries. Rep. Math. Phys., Vol. 5, 1974, pp. 219-280. Zbl0296.35021MR376004
3. [3] E Balslev, Schrödinger operators with symmetries. II. Rep. Math. Phys., Vol. 5, 1974, pp. 393-413. Zbl0296.35022MR376005
4. [4] H.L. Cycon, R.G. Froese, Werner Kirsch, and Barry Simon. Schrödinger Operators with Application to Quantum Mechanics and Global Geometry. Text and Monographs in Physics. Springer-Verlag, Berlin, 1 edition, 1987. Zbl0619.47005MR883643
5. [5] W.D. Evans, R.T. Lewis and Y. Saitö, The Agmon spectral function for molecular hamiltonians with symmetry restrictions. Proc. Royal Soc. Lond. A, Vol. 440, 1993, pp. 621-638. Zbl0804.35028MR1220214
6. [6] W. Hunziker, On the spectra of Schrödinger multiparticle Hamiltonians. Helv. Phys. Acta, Vol. 39, 1966, pp. 451-462. Zbl0141.44701MR211711
7. [7] K. Jörgens and J. Weidmann, Spectral Properties of Hamiltonian Operators, Vol. 313 of Lecture Notes in Mathematics.Springer-Verlag, Berlin, 1 edition, 1973. Zbl0248.35002MR492941
8. [8] E.H. Lieb, M. Loss, and H. Siedentop, Stability of Relativistic Matter via Thomas-Fermi Theory. Helv. Phys. Acta, In press. Zbl0866.47050MR1428033
9. [9] E.H. Lieb and Horng-Ter Yau, The stability and instability of relativistic matter. Commun. Math. Phys., Vol. 118, 1988, pp. 177-213. Zbl0686.35099MR956165
10. [10] F.W.J. Olver, Bessel functions of integer order. In Milton Abramowitz and Irene A. Stegun, editors, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, chapter 9, pp. 355-433. Dover Publications, New York, 5 edition, 1968. MR208797
11. [11] A. Persson, Bounds for the discrete spectrum of a semi-bounded Schrödinger operator. Math. Scand., Vol. 8, pp. 143-153, 1960. Zbl0145.14901MR133586
12. [12] M. Reed and B. Simon, Methods of Modern Mathematical Physics, volume 4: Analysis of Operators. Academic Press, New York, 1 edition, 1978. Zbl0401.47001
13. [13] B. Simon, Quantum Mechanics for Hamiltonians Defined as Quadratic Forms. Princeton University Press, Princeton, New Jersey, 1 edition, 1971. Zbl0232.47053MR455975
14. [ 14] B. Simon, Trace Ideals and Their Applications. Number 35 in London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 1979. Zbl0423.47001MR541149
15. [15] W. Thirring, Lehrbuch der Mathematischen Physik 3: Quantenmechanik von Atomen und Molekülen. Springer-Verlag, Wien, New York, 1 edition, 1979. Zbl0408.46054MR537034
16. [16] C. Van Winter, Theory of finite systems of particles I. the Green function. Mat. Fys. Dan. Vid. Selsk., Vol. 2(8), 1964, pp. 1-60. Zbl0122.22403MR201168
17. [17] S.A. Vugalter and G.M. Zhislin, On the finiteness of discrete spectrum in the n-particle problem. Rep. Math. Phys., Vol. 19(1), February 1984, pp. 39-90. Zbl0581.46063MR740347
18. [18] G.M. Zislin, A study of the spectrum of the Schrödinger operator for a system of several particles. Trudy Moskov. Mat. Obsc., Vol. 9, 1960, pp. 81-120. MR126729
19. [19] G.M. Zislin, Spectrum of differential operators of quantum-mechanical many-particle systems in spaces of functions of a given symmetry. Mathematics of the USSR-Izvestija, Vol. 3(3), 1969, pp. 559-616. Zbl0205.14503