Geodesic
Singular numbers of a~weighted convolution operator
Sbornik. Mathematics, Tome 61 (1988) no. 2, pp. 309-319

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

This article studies a convolution operator on $[0,2\pi]$ with $2\pi$-periodic kernel. The operator acts from $L_2(0,2\pi)$ to $L_2(0,2\pi;\mu)$ where $\mu$ is a Borel measure. An asymptotic formula is obtained for the singular numbers in the case of kernels satisfying a certain regularity condition and of measures with continuous densities. Examples and counterexamples are given. Bibliography: 7 titles. 
@article{SM_1988_61_2_a2,
     author = {O. G. Parfenov},
     title = {Singular numbers of a~weighted convolution operator},
     journal = {Sbornik. Mathematics},
     pages = {309--319},
     publisher = {mathdoc},
     volume = {61},
     number = {2},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_61_2_a2/}
}
TY  - JOUR
AU  - O. G. Parfenov
TI  - Singular numbers of a~weighted convolution operator
JO  - Sbornik. Mathematics
PY  - 1988
SP  - 309
EP  - 319
VL  - 61
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1988_61_2_a2/
LA  - en
ID  - SM_1988_61_2_a2
ER  - 
%0 Journal Article
%A O. G. Parfenov
%T Singular numbers of a~weighted convolution operator
%J Sbornik. Mathematics
%D 1988
%P 309-319
%V 61
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1988_61_2_a2/
%G en
%F SM_1988_61_2_a2
O. G. Parfenov. Singular numbers of a~weighted convolution operator. Sbornik. Mathematics, Tome 61 (1988) no. 2, pp. 309-319. http://geodesic.mathdoc.fr/item/SM_1988_61_2_a2/