Geodesic
Uniqueness and nonuniqueness of solution of the totality of the first kind equations equivalent with respect to a~given accuracy
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 5 (1998), pp. 85-96

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A linear equation of the first kind with a perturbed operator is considered. It is assumed that a level of perturbation is known. The totality of equations equivalent with respect to a given accuracy is introduced. For such a totality, new definitions of uniqueness and nonuniqueness are formulated. Algorithms for investigation of the (non)uniqueness are constructed. Examples of applications are given in the X-ray structural analysis and the diffraction method. 
@article{TIMM_1998_5_a7,
     author = {A. L. Ageev},
     title = {Uniqueness and nonuniqueness of solution of the totality of the first kind equations equivalent with respect to a~given accuracy},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {85--96},
     publisher = {mathdoc},
     volume = {5},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_1998_5_a7/}
}
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A. L. Ageev. Uniqueness and nonuniqueness of solution of the totality of the first kind equations equivalent with respect to a~given accuracy. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 5 (1998), pp. 85-96. http://geodesic.mathdoc.fr/item/TIMM_1998_5_a7/