Geodesic
A new representation of Hankel operators and its spectral consequences
Algebra i analiz, Tome 30 (2018) no. 3, pp. 286-310.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper, the Hankel operators $H$ are represented as pseudo-differential operators $A$ in the space of functions defined on the whole axis. The amplitudes of such operators $A$ have a very special structure: they are products of functions of a one variable only. This representation has numerous spectral consequences, both for compact Hankel operators and for operators with the continuous spectrum.
Keywords: Hankel operators, spectral properties, absolutely continuous and discrete spectra, asymptotics of eigenvalues. 
@article{AA_2018_30_3_a13,
     author = {D. R. Yafaev},
     title = {A new representation of {Hankel} operators and its spectral consequences},
     journal = {Algebra i analiz},
     pages = {286--310},
     publisher = {mathdoc},
     volume = {30},
     number = {3},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AA_2018_30_3_a13/}
}
TY  - JOUR
AU  - D. R. Yafaev
TI  - A new representation of Hankel operators and its spectral consequences
JO  - Algebra i analiz
PY  - 2018
SP  - 286
EP  - 310
VL  - 30
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2018_30_3_a13/
LA  - en
ID  - AA_2018_30_3_a13
ER  - 
%0 Journal Article
%A D. R. Yafaev
%T A new representation of Hankel operators and its spectral consequences
%J Algebra i analiz
%D 2018
%P 286-310
%V 30
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2018_30_3_a13/
%G en
%F AA_2018_30_3_a13
D. R. Yafaev. A new representation of Hankel operators and its spectral consequences. Algebra i analiz, Tome 30 (2018) no. 3, pp. 286-310. http://geodesic.mathdoc.fr/item/AA_2018_30_3_a13/

[1] Birman M. Sh., Solomyak M. Z., “Asimptotika spektra slabo polyarnykh integralnykh operatorov”, Izv. AN SSSR. Ser. mat., 34:5 (1970), 1142–1158 | MR | Zbl

[2] Birman M. Sh., Solomyak M. Z., “Spektralnaya asimptotika negladkikh ellipticheskikh operatorov. I”, Tr. Mosk. mat. o-va, 27, 1972, 3–52 ; “II”, Тр. Моск. мат. о-ва, 28, 1973, 3–34 | MR | Zbl | MR | Zbl

[3] Birman M. Sh., Solomyak M. Z., “Asimptotika spektra psevdodifferentsialnykh operatorov s anizotropno-odnorodnymi simvolami. I”, Vestn. Leningr. un-ta. Ser. mat., mekh., astronom., 1977, no. 3, 13–21 ; “II”, Вестн. Ленингр. ун-та. Сер. мат., мех., астроном., 1979, No 3, 5–10 | Zbl | Zbl

[4] Birman M. Sh., Solomyak M. Z., Spektralnaya teoriya samosopryazhennykh operatorov v gilbertovom prostranstve, LGU, L., 1980 | MR

[5] Erdelyi A., “General asymptotic expansions of Laplace integrals”, Arch. Rational Mech. Anal., 7:1 (1961), 1–20 | DOI | MR | Zbl

[6] Glover K., Lam J., Partington J. R., “Rational approximation of a class of infinite-dimensional systems. I. Singular values of Hankel operators”, Math. Control Signals Systems, 3:4 (1990), 325–344 | DOI | MR | Zbl

[7] Nikolski N. K., Operators, functions, and systems: an easy reading, v. I, Math. Surv. Monogr., 92, Hardy, Hankel, and Toeplitz, Amer. Math. Soc., Providence, RI, 2002 | MR | Zbl

[8] Peller V. V., Hankel operators and their applications, Springer Monogr. Math., Springer-Verlag, New York, 2003 | DOI | MR | Zbl

[9] Pushnitski A., Yafaev D., “Sharp estimates for singular values of Hankel operators”, Integral Equations Operator Theory, 83:3 (2015), 393-411 | DOI | MR | Zbl

[10] Pushnitski A., Yafaev D., “Asymptotic behavior of eigenvalues of Hankel operators”, Int. Math. Res. Not. IMRN, 2015:22 (2015), 11861–11886 | MR | Zbl

[11] Pushnitski A., Yafaev D., “Localization principle for compact Hankel operators”, J. Funct. Anal., 270:9 (2016), 3591–3621 | DOI | MR | Zbl

[12] Pushnitski A., Yafaev D., “Spectral asymptotics for compact selfadjoint Hankel operators”, J. Spectr. Theory, 6:4 (2016), 921–953 | DOI | MR | Zbl

[13] Pushnitski A., Yafaev D., “Best rational approximation of functions with logarithmic singularities”, Constr. Approx., 46:2 (2017), 243–269 | DOI | MR | Zbl

[14] Widom H., “Hankel matrices”, Trans. Amer. Math. Soc., 121 (1966), 1–35 | DOI | MR | Zbl

[15] Yafaev D. R., “Diagonalizations of two classes of unbounded Hankel operators”, Bull. Math. Sci., 4:2 (2014), 175–198 | DOI | MR | Zbl

[16] Yafaev D. R., “Criteria for Hankel operators to be sign-definite”, Anal. PDE, 8:1 (2015), 183–221 | DOI | MR | Zbl

[17] Yafaev D. R., “On finite rank Hankel operators”, J. Funct. Anal., 268:7 (2015), 1808–1839 | DOI | MR | Zbl

[18] Yafaev D. R., “Quasi-Carleman operators and their spectral properties”, Integral Equations Operator Theory, 81:4 (2015), 499–534 | DOI | MR | Zbl

[19] Yafaev D. R., “Quasi-diagonalization of Hankel operators”, J. Anal. Math., 29 (2017), 133–182 | DOI | MR

[20] Yafaev D. R., “Spectral and scattering theory for differential and Hankel operator”, Adv. Math., 308 (2017), 713–766 | DOI | MR | Zbl