Geodesic
Singular integral equations of nonclassical type on a piecewise smooth curve
Matematičeskie zametki SVFU, Tome 29 (2022), pp. 37-61.

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We consider singular integral operators on a piecewise smooth curve in weighted Lebesgue and Hölder spaces with piecewise continuous matrix coefficients. In contrast to the classical case, these operators, in addition to the singular Cauchy operator, also contain non-compact integral operators of a special form which are defined by the kernel that is approximately homogeneous of degree $-1$ with respect to distances to the nodes of the curve. Similar operators arise in many applications. A criterion for the Fredholm property of these operators is obtained and a formula for their index is given.
Keywords: singular integral operator, piecewise smooth contour, weighted Lebesgueand Höolder spaces, singular Cauchy operator, integral operator with kernel homogeneousof degree $-1$, Fredholm criterion
Mots-clés : index formula. 
@article{SVFU_2022_29_a3,
     author = {A. P. Soldatov},
     title = {Singular integral equations of nonclassical type on a piecewise smooth curve},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {37--61},
     publisher = {mathdoc},
     volume = {29},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2022_29_a3/}
}
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A. P. Soldatov. Singular integral equations of nonclassical type on a piecewise smooth curve. Matematičeskie zametki SVFU, Tome 29 (2022), pp. 37-61. http://geodesic.mathdoc.fr/item/SVFU_2022_29_a3/