On the Perturbation of Self-Adjoint Operators with Absolutely Continuous Spectrum
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2013) no. 3, pp. 392-399 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The perturbation of the linear self-adjoint operator with absolutely continuous spectrum is studied and the inverse problem on finding the perturbation by the given spectrum is solved.
@article{JMAG_2013_9_3_a6,
     author = {A. N. Syrovatsky},
     title = {On the {Perturbation} of {Self-Adjoint} {Operators} with {Absolutely} {Continuous} {Spectrum}},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {392--399},
     year = {2013},
     volume = {9},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2013_9_3_a6/}
}
TY  - JOUR
AU  - A. N. Syrovatsky
TI  - On the Perturbation of Self-Adjoint Operators with Absolutely Continuous Spectrum
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2013
SP  - 392
EP  - 399
VL  - 9
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JMAG_2013_9_3_a6/
LA  - en
ID  - JMAG_2013_9_3_a6
ER  - 
%0 Journal Article
%A A. N. Syrovatsky
%T On the Perturbation of Self-Adjoint Operators with Absolutely Continuous Spectrum
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2013
%P 392-399
%V 9
%N 3
%U http://geodesic.mathdoc.fr/item/JMAG_2013_9_3_a6/
%G en
%F JMAG_2013_9_3_a6
A. N. Syrovatsky. On the Perturbation of Self-Adjoint Operators with Absolutely Continuous Spectrum. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2013) no. 3, pp. 392-399. http://geodesic.mathdoc.fr/item/JMAG_2013_9_3_a6/

[1] N. I. Akhiezer, Lectures on Integral Transforms, AMS, Providence, RI, 1988 | MR | Zbl

[2] N. I. Akhiezer, I. M. Glazman, Theory of Linear Operators in Hilbert Space, v. 1, Vyshcha shkola, Kharkiv, 1977 (Russian) | MR

[3] N. I. Akhiezer, The Classical Moment Problem and Some Related Questions in Analysis, Gos. Izd. Fiz.-Mat. Lit., M., 1961 (Russian)

[4] K. O. Friedrichs, “Uber die Spektralzerlegung eines Integral-operators”, Math. Ann., 115 (1938), 259–272 | DOI | MR

[5] F. D. Gakhov, Boundary Value Problems, 3d ed., Nauka, M., 1977 (Russian) | MR

[6] T. Kato, Perturbation Theory of Linear Operators, Mir, M., 1972 (Russian) | MR | Zbl

[7] F. Rellich, “Storumgtheory der Spektralzerlegung, I”, Math. Ann., 113 (1936), 600–619 | DOI | MR

[8] M. Rozenblum, “Perturbation of the Continuous Spectrum and Unitary Equivalence”, Pacif. J. Math., 7:1 (1957), 997–1010 | DOI | MR

[9] H. Weyl, “Uber Beschrankte Quadratishe Formen, deren Differenz Vollstetig ist”, Rend. Circolo Mat. Palermo, 27 (1909), 373–392 | DOI | Zbl