Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 36, Tome 318 (2004), pp. 298-307
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N. Filonov; A. V. Sobolev. Absence of the singular continuous component in the spectrum of analytic direct integrals. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 36, Tome 318 (2004), pp. 298-307. http://geodesic.mathdoc.fr/item/ZNSL_2004_318_a14/
@article{ZNSL_2004_318_a14,
author = {N. Filonov and A. V. Sobolev},
title = {Absence of the singular continuous component in the spectrum of analytic direct integrals},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {298--307},
year = {2004},
volume = {318},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_318_a14/}
}
TY - JOUR
AU - N. Filonov
AU - A. V. Sobolev
TI - Absence of the singular continuous component in the spectrum of analytic direct integrals
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2004
SP - 298
EP - 307
VL - 318
UR - http://geodesic.mathdoc.fr/item/ZNSL_2004_318_a14/
LA - en
ID - ZNSL_2004_318_a14
ER -
%0 Journal Article
%A N. Filonov
%A A. V. Sobolev
%T Absence of the singular continuous component in the spectrum of analytic direct integrals
%J Zapiski Nauchnykh Seminarov POMI
%D 2004
%P 298-307
%V 318
%U http://geodesic.mathdoc.fr/item/ZNSL_2004_318_a14/
%G en
%F ZNSL_2004_318_a14
We give a simple proof of the absence of the singular continuous component in the spectrum of self-adjoint operators representable as analytic direct integrals.
[2] J. Math. Science, 106:3 (2001), 3078–3086 | DOI | MR | Zbl
[3] N. Filonov, F. Klopp, “Absolute continuity of the spectrum of a Schrödinger operator with a potential which is periodic in some directions and decays in others”, Documenta Mathematica, 9 (2004), 107–121 | MR | Zbl
[4] C. Gérard, F. Nier, “The Mourre theory for analytically fibered operators”, J. Funct. Anal., 152:1 (1998), 202–219 | DOI | MR | Zbl
[5] R. Hempel, I. Herbst, “Bands and gaps for periodic magnetic Hamiltonians”, Operator Theory: Advances and Applications, 78, Birkhäuser, 1995, 175–184 | MR | Zbl
[6] P. Kuchment, Floquet theory for partial differential equations, Birkhäuser, Basel, 1993 | MR | Zbl