Geodesic
Upper estimates for the approximation numbers of the generalized Laplace transform
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and equations of mathematical physics, Tome 283 (2013), pp. 267-287.

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

A Laplace-transform-type operator $\mathcal L$ acting in the Lebesgue spaces of real functions on the half-axis is considered. Sufficient conditions under which $\mathcal L$ belongs to some Schatten-type classes are found. Upper asymptotic estimates for the approximation numbers of $\mathcal L$ are obtained. 
@article{TM_2013_283_a17,
     author = {E. P. Ushakova},
     title = {Upper estimates for the approximation numbers of the generalized {Laplace} transform},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {267--287},
     publisher = {mathdoc},
     volume = {283},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2013_283_a17/}
}
TY  - JOUR
AU  - E. P. Ushakova
TI  - Upper estimates for the approximation numbers of the generalized Laplace transform
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2013
SP  - 267
EP  - 287
VL  - 283
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2013_283_a17/
LA  - ru
ID  - TM_2013_283_a17
ER  - 
%0 Journal Article
%A E. P. Ushakova
%T Upper estimates for the approximation numbers of the generalized Laplace transform
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2013
%P 267-287
%V 283
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2013_283_a17/
%G ru
%F TM_2013_283_a17
E. P. Ushakova. Upper estimates for the approximation numbers of the generalized Laplace transform. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and equations of mathematical physics, Tome 283 (2013), pp. 267-287. http://geodesic.mathdoc.fr/item/TM_2013_283_a17/

[1] Allakhverdiev D.E., “O skorosti priblizheniya vpolne nepreryvnykh operatorov konechnomernymi operatorami”, Uchen. zap. Azerb. un-ta, 1957, no. 2, 27–35

[2] Bennett C., Sharpley R., Interpolation of operators, Pure Appl. Math., 129, Acad. Press, New York, 1988 | MR | Zbl

[3] Birman M.Sh., Solomyak M.Z., “Otsenki singulyarnykh chisel integralnykh operatorov”, UMN., 32:1 (1977), 17–84 | MR | Zbl

[4] Birman M.Sh., Solomyak M.Z., Spektralnaya teoriya samosopryazhennykh operatorov v gilbertovom prostranstve, Izd-vo Leningr. un-ta, L., 1980 | MR

[5] Edmunds D.E., Evans W.D., Harris D.J., “Approximation numbers of certain Volterra integral operators”, J. London Math. Soc. Ser. 2, 37:3 (1988), 471–489 | DOI | MR | Zbl

[6] Edmunds D.E., Evans W.D., Harris D.J., “Two-sided estimates for the approximation numbers of certain Volterra integral operators”, Stud. math., 124:1 (1997), 59–80 | MR | Zbl

[7] Edmunds D.E., Stepanov V.D., “The measure of non-compactness and approximation numbers of certain Volterra integral operators”, Math. Ann., 298 (1994), 41–66 | DOI | MR | Zbl

[8] Evans W.D., Harris D.J., Lang J., “Two-sided estimates for the approximation numbers of Hardy-type operators in $L^\infty $ and $L^1$”, Stud. math., 130:2 (1988), 171–192 | MR

[9] Gokhberg I.Ts., Krein M.G., Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov v gilbertovom prostranstve, Nauka, M., 1965 | MR

[10] Gol'dman M.L., Heinig H.P., Stepanov V.D., “On the principle of duality in Lorentz spaces”, Can. J. Math., 48:5 (1996), 959–979 | DOI | MR | Zbl

[11] König H., Eigenvalue distribution of compact operators, Birkhäuser, Basel, 1986 | MR

[12] Lifshits M.A., Linde W., Approximation and entropy numbers of Volterra operators with Applications to Brownian motion, Mem. AMS, 157, no. 745, Amer. Math. Soc., Providence, RI, 2002 | MR

[13] Lomakina E.N., “Otsenki approksimativnykh chisel odnogo klassa integralnykh operatorov. I”, Sib. mat. zhurn., 44:1 (2003), 178–192 | MR | Zbl

[14] Lomakina E.N., “Otsenki approksimativnykh chisel odnogo klassa integralnykh operatorov. II”, Sib. mat. zhurn., 44:2 (2003), 372–388 | MR | Zbl

[15] Lomakina E.N., Stepanov V.D., “On asymptotic behaviour of the approximation numbers and estimates of Schatten–von Neumann norms of the Hardy-type integral operators”, Function spaces and applications (New Delhi, 1997), Narosa, New Delhi, 2000, 153–187 | MR | Zbl

[16] Lomakina E.N., Stepanov V.D., “Asimptoticheskie otsenki approksimativnykh i entropiinykh chisel odnovesovogo operatora Rimana–Liuvillya”, Mat. trudy, 9:1 (2006), 52–100 | MR | Zbl

[17] Mazya V.G., Prostranstva S.L. Soboleva, Izd-vo LGU, L., 1985 | MR | Zbl

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

[19] Pietsch A., Eigenvalues and s-numbers, Cambridge Stud. Adv. Math., 13, Cambridge Univ. Press, Cambridge, 1987 | MR | Zbl

[20] Sinnamon G., Stepanov V.D., “The weighted Hardy inequality: New proofs and the case $p=1$”, J. London Math. Soc. Ser. 2, 54 (1996), 89–101 | DOI | MR | Zbl

[21] Stepanov V.D., “On the lower bounds for Schatten–von Neumann norms of certain Volterra integral operators”, J. London Math. Soc. Ser. 2, 61 (2000), 905–922 | DOI | MR | Zbl

[22] Stepanov V.D., Ushakova E.P., “Vesovye otsenki dlya integralnykh operatorov na poluosi s monotonnymi yadrami”, Sib. mat. zhurn., 45:6 (2004), 1378–1390 | MR | Zbl

[23] Ushakova E.P., “O singulyarnykh chislakh obobschennogo preobrazovaniya Stiltesa”, DAN, 431:2 (2010), 175–176 | MR | Zbl

[24] Ushakova E.P., “Otsenki singulyarnykh chisel preobrazovanii tipa Stiltesa”, Sib. mat. zhurn., 52:1 (2011), 201–209 | MR | Zbl

[25] Ushakova E.P., “On compactness of Laplace and Stieltjes type transformations in Lebesgue spaces”, J. Oper. Theory, 69:2 (2013), 511–524 | DOI | MR | Zbl