Geodesic
On the regularization of an equation of the first kind with a multiple integration operator
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 4, pp. 578-586

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The zero-order Tikhonov regularization method as applied to an equation of the first kind with a multiple differentiation operator is considered for the case when the solution belongs to a class from the domain of the adjoint operator. An estimate of the error of the approximate solution in the uniform metric is obtained, which is sharp with respect to the order, and the order is established. It is proved that the proposed method is optimal with respect to the order. Unimprovable estimates of the order of the modulus of continuity of the inverse operator are obtained. 
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     author = {S. Yu. Sovetnikova and G. V. Khromova},
     title = {On the regularization of an equation of the first kind with a~multiple integration operator},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
     volume = {47},
     number = {4},
     year = {2007},
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     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_4_a1/}
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S. Yu. Sovetnikova; G. V. Khromova. On the regularization of an equation of the first kind with a multiple integration operator. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 4, pp. 578-586. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_4_a1/