Geodesic
Investigation of methods of localization of $q$-jumps and discontinities of firsth king of noisy function
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2019), pp. 3-14

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We consider the problem of localizing (determination of position) of discontinuities of the first kind of a function of one variable and the problem of localizing $q$-jumps of a noisy function. In the first case it is assumed that the exact function is smooth except for a finite number of discontinuities of the first kind. In the second case, the exact function is smooth except for a finite number of small segments of length $2q$. It is required that the number of discontinuities ($q$-jumps) be determined and approximated their position from an approximately given function and the level of the perturbation in $L_2(\mathbb{R})$. We construct a class of regular averaging methods and obtain and estimates of the accuracy of localization, separability, and observability on classes of correctness.
Keywords: ill-posed problems, regularizing method, separation threshold, threshold of observability, discontinuity of the first kind, $q$-jump. 
@article{IVM_2019_7_a0,
     author = {A. L. Ageev and T. V. Antonova},
     title = {Investigation of methods of localization of $q$-jumps and discontinities of firsth king of noisy function},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--14},
     publisher = {mathdoc},
     number = {7},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_7_a0/}
}
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A. L. Ageev; T. V. Antonova. Investigation of methods of localization of $q$-jumps and discontinities of firsth king of noisy function. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2019), pp. 3-14. http://geodesic.mathdoc.fr/item/IVM_2019_7_a0/