On the singular spectrum of discrete Schrödinger operator

S. Naboko

Séminaire Équations aux dérivées partielles (Polytechnique) (1993-1994)

  • page 1-9

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Naboko, S.. "On the singular spectrum of discrete Schrödinger operator." Séminaire Équations aux dérivées partielles (Polytechnique) (1993-1994): 1-9. <http://eudml.org/doc/112076>.

@article{Naboko1993-1994,
author = {Naboko, S.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {singular spectrum; bounded discrete Schrödinger operator; Friedrichs model operators},
language = {eng},
pages = {1-9},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {On the singular spectrum of discrete Schrödinger operator},
url = {http://eudml.org/doc/112076},
year = {1993-1994},
}

TY - JOUR
AU - Naboko, S.
TI - On the singular spectrum of discrete Schrödinger operator
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1993-1994
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 9
LA - eng
KW - singular spectrum; bounded discrete Schrödinger operator; Friedrichs model operators
UR - http://eudml.org/doc/112076
ER -

References

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  4. [4] R. Edwards - Fourier series, a modern introductionSpringer-Verlag (1979). Zbl0424.42001
  5. [5] B. Simon - Some Jacobi matrices with decaying potential and dense point spectrumComm. in Math. Phys.87 (1982), 253-258. Zbl0546.35048MR684102
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  7. [7] B. Simon and T. Spencer - Trace class perturbations and the absence of absolutely continuous spectraComm. in Math. Phys.125 (1989), 113-126. Zbl0684.47010MR1017742
  8. [8] M. Reed and B. Simon - Methods of modern mathematical physics 4 (Analysis of operators)Acad. Press (1977). Zbl0401.47001MR493422
  9. [9] S. Albeverio - On bound states in the continum of N-body system and the virial theoremAnn. Phys.71 (1972), 167-276. MR300574
  10. [10] S.N. Naboko - Uniqueness theorems for operator-valued functions with positive imaginary part, and the singular spectrum in the selfadjointFriedrichs model Arkiv for Matem. 23:1 (1987), 115-140. Zbl0632.47012MR918381
  11. [11] S.N. Naboko and S.I. Yakovlev - Discrete Schrödinger operator, point spectrum on a continuous one Algebra andAnalysis4:3 (1992), 183-195 (in Russian). Zbl0828.39005MR1190777
  12. [12] I.C. Gohberg and M.G. Krein - Introduction to the theory of linear nonselfadjoint operators in Hilbert spaceAmer. Math. Soc.Providence R. I. (1969). Zbl0181.13504MR246142
  13. [13] B.S. Pavlov and S.V. Petras - On the singular spectrum of weakly perturbed operator of multiplication, Funk. Anal. i Priloz4:2 (1970), 54-61 (in Russian) ; English. transl. in Functional Anal. Appl.4 (1970). Zbl0206.43801MR265983
  14. [14] L.D. Faddeev - On Friedrichs model in continuous spectrum perturbation theoryTrudy Math. Inst. Acad. of Sci. USSR73 (1964) 292-313 (in Russian) ; English transl. in Amer. Math. Soc. Transl.62 (1967). Zbl0148.12801MR178362
  15. [15] L.D. Faddeev and B.S. Pavlov - Zero sets of operator-functions with positive imaginary part Lecture Notes in Math. Springer-Verlag, 1043 (1984) 124-128. 
  16. [16] W.K. Heyman and P.B. Kennedy - Subharmonicfunctions 1, Acad. Press (1976). 
  17. [17] S.I. Yakovlev - Spectral analysis of selfadjoint operators in Friedrichs model S.-Petersburg Univ. Depart. Math. Phys. Thesis (1991). 
  18. [18] V. Lance - Nonselfadjoint difference operator, Dokl. Acad. Sci. USSR, 173:6 (1967), 1260-1263 (in Russian). MR211028
  19. [19] E.M. Dynkin, S.N. Naboko and S.I. Yakovlev - The boundary of finiteness of the singular spectrum in the selfadjoint Friedrichs model, Algebra and Analysis, 3:2 (1991) (in Russian) ; English transl. in St. Petersburg Math. J.3:2 (1992) 299-311. Zbl0791.47001MR1137522

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