Geodesic
$C^*$-Algebra of Integral Operators with Homogeneous Kernels and Oscillating Coefficients
Matematičeskie zametki, Tome 99 (2016) no. 3, pp. 323-332

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We consider the $C^*$-algebra generated by multidimensional integral operators with $(-n)$th-order homogeneous kernels and by the operators of multiplication by oscillating coefficients of the form $|x|^{i\alpha}$. For this algebra, we construct an operator symbolic calculus and obtain necessary and sufficient conditions for the Fredholm property of an operator in terms of this calculus.
Keywords: integral operator, $C^*$-algebra, operator with oscillating coefficients, symbolic calculus, Fredholm property
Mots-clés : index formula. 
@article{MZM_2016_99_3_a0,
     author = {O. G. Avsyankin},
     title = {$C^*${-Algebra} of {Integral} {Operators} with {Homogeneous} {Kernels} and {Oscillating} {Coefficients}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {323--332},
     publisher = {mathdoc},
     volume = {99},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_3_a0/}
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O. G. Avsyankin. $C^*$-Algebra of Integral Operators with Homogeneous Kernels and Oscillating Coefficients. Matematičeskie zametki, Tome 99 (2016) no. 3, pp. 323-332. http://geodesic.mathdoc.fr/item/MZM_2016_99_3_a0/