On the Simon–Spencer theorem
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 4 (2008) no. 1, pp. 108-120 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper presents a generalization of the classical result by B. Simon and T. Spencer on the absence of absolutely continuous spectrum for the continuous one-dimensional Schrödinger operator with an unbounded potential.
@article{JMAG_2008_4_1_a4,
     author = {A. Gordon and J. Holt and A. Laptev and S. Molchanov},
     title = {On the {Simon{\textendash}Spencer} theorem},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {108--120},
     year = {2008},
     volume = {4},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2008_4_1_a4/}
}
TY  - JOUR
AU  - A. Gordon
AU  - J. Holt
AU  - A. Laptev
AU  - S. Molchanov
TI  - On the Simon–Spencer theorem
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2008
SP  - 108
EP  - 120
VL  - 4
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JMAG_2008_4_1_a4/
LA  - en
ID  - JMAG_2008_4_1_a4
ER  - 
%0 Journal Article
%A A. Gordon
%A J. Holt
%A A. Laptev
%A S. Molchanov
%T On the Simon–Spencer theorem
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2008
%P 108-120
%V 4
%N 1
%U http://geodesic.mathdoc.fr/item/JMAG_2008_4_1_a4/
%G en
%F JMAG_2008_4_1_a4
A. Gordon; J. Holt; A. Laptev; S. Molchanov. On the Simon–Spencer theorem. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 4 (2008) no. 1, pp. 108-120. http://geodesic.mathdoc.fr/item/JMAG_2008_4_1_a4/

[1] M. Eastham, “On a Limit-Point Method of Hartman”, Bull. London Math. Soc., 4 (1972), 340–344 | DOI | MR | Zbl

[2] I. Glazman, Direct Methods of Qualitative Spectral Analysis of Singular Differential Operators, Israel Progr. for Sci. Transl., Jerusalem, 1965 | MR | Zbl

[3] A. Gordon, S. Molchanov, B. Tsagani, “Spectral Theory for One-Dimensional Schrödinger Operators with Strongly Fluctuating Potentials”, Funct. Anal. Appl., 25 (1992), 236–238 | DOI | MR | Zbl

[4] P. Hartman, “The Number of $L^2$-Solutions of $x''+q(t)x=0$”, Amer. J. Math., 43 (1951), 635–645 | DOI | MR

[5] T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Springer-Verlag, Berlin, Heidelberg, 1995 | MR

[6] H. McKean, Stochastic Integrals, Acad. Press, New York, 1969 | MR | Zbl

[7] S. Molchanov, “Multiscale Averaging for Ordinary Differential Equations. Homogenization Series on Advances in Mathematics for Applied Sciences”, World Sci., 50 (1999), 316–397 | MR | Zbl

[8] M. Reed, B. Simon, Methods of Modern Mathematical Physics. II. Fourier Analysis, Self-Adjointness, Acad. Press, London, 1975 | MR | Zbl

[9] B. Simon, T. Spencer, “Trace Class Perturbations and the Absence of Absolutely Continuous Spectrum”, Comm. Math. Phys., 87 (1982), 253–258 | DOI | MR | Zbl

[10] B. Simon, G. Stolz, “Operators with Singular Continuous Spectrum. V. Sparse Potentials”, Amer. Math. Soc., 124 (1996), 2073–2080 | DOI | MR | Zbl