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Spectral properties of many-body Schrödinger operators with dilatation- analytic interactions. (English) Zbl 0219.47005

MSC:
47A10Spectrum and resolvent of linear operators
47N50Applications of operator theory in quantum physics
35J10Schrödinger operator
47A20Dilations, extensions and compressions of linear operators
References:
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[4]Dollard, J.: J. Math. Phys.5, 729 (1964). · doi:10.1063/1.1704171
[5]Buslaev” Matreev, J.: Theoret. Math. Phys. (Russian), 1970.
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[8]Combes, J.M.: Relatively compact interactions in many particle systems. Commun. Math. Phys.12, 283 (1969). · Zbl 0174.28304 · doi:10.1007/BF01667314
[9]Hunziker, W.: On the spectra of Schrödinger multiparticle Hamiltonians. Helv. Phys. Acta39, 5, 451–462 (1966).
[10]Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer 1966.
[11]Nelson, E.: Analytic vectors. Ann. Math.70, 3 (1959). · Zbl 0091.10704 · doi:10.2307/1970331
[12]Steinberg, S.: Arc. for Rat. Mechs. Anal.31 372 (1968). · Zbl 0167.43002 · doi:10.1007/BF00251419
[13]Wolf, F.: On the essential spectrum of partial differential boundary problems. Commun. Pure Appl. Math.12, 211–228 (1959). · Zbl 0087.30501 · doi:10.1002/cpa.3160120202
[14]Simon, B.: On the infinitude or finiteness of the number of bound states of ann-body quantum system, Preprint, Princeton University 1970.
[15]Ichinose, T.: On operators on tensor products of Banach spaces, Preprint, Nagoya University.