Geodesic
On the Algebra of Multidimensional Integral Operators with Homogeneous $SO(n)$-Invariant Kernels and Weakly Radially Oscillating Coefficients
Matematičeskie zametki, Tome 82 (2007) no. 2, pp. 163-176

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

In this paper, we study the Banach algebra $\mathfrak B$ generated by multidimensional integral operators whose kernels are homogeneous functions of degree $(-n)$ invariant with respect to the rotation group $SO(n)$ and by the operators of multiplication by radial weakly oscillating functions. A symbolic calculus is developed for the algebra $\mathfrak B$. The Fredholm property and the formula for calculating the index are described in terms of this calculus.
Keywords: Fredholm property, integral operators, operator algebra, index of a Fredholm operator, Banach algebra, locally oscillating function. 
@article{MZM_2007_82_2_a0,
     author = {O. G. Avsyankin and V. M. Deundyak},
     title = {On the {Algebra} of {Multidimensional} {Integral} {Operators} with {Homogeneous} $SO(n)${-Invariant} {Kernels} and {Weakly} {Radially} {Oscillating} {Coefficients}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {163--176},
     publisher = {mathdoc},
     volume = {82},
     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_2_a0/}
}
TY  - JOUR
AU  - O. G. Avsyankin
AU  - V. M. Deundyak
TI  - On the Algebra of Multidimensional Integral Operators with Homogeneous $SO(n)$-Invariant Kernels and Weakly Radially Oscillating Coefficients
JO  - Matematičeskie zametki
PY  - 2007
SP  - 163
EP  - 176
VL  - 82
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_82_2_a0/
LA  - ru
ID  - MZM_2007_82_2_a0
ER  - 
%0 Journal Article
%A O. G. Avsyankin
%A V. M. Deundyak
%T On the Algebra of Multidimensional Integral Operators with Homogeneous $SO(n)$-Invariant Kernels and Weakly Radially Oscillating Coefficients
%J Matematičeskie zametki
%D 2007
%P 163-176
%V 82
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2007_82_2_a0/
%G ru
%F MZM_2007_82_2_a0
O. G. Avsyankin; V. M. Deundyak. On the Algebra of Multidimensional Integral Operators with Homogeneous $SO(n)$-Invariant Kernels and Weakly Radially Oscillating Coefficients. Matematičeskie zametki, Tome 82 (2007) no. 2, pp. 163-176. http://geodesic.mathdoc.fr/item/MZM_2007_82_2_a0/