On a Sufficient Condition for Regularizability of Linear Inverse Problem
Matematičeskie zametki, Tome 82 (2007) no. 2, pp. 242-246
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We study the regularizability of mappings inverse to continuous linear operators from $C(0,1)$ into $L_2(0,1)$ and obtain a sufficient condition for the regularizability of such mappings in terms of the properties of the extended operator. We show that the obtained condition is in a sense exact.
Keywords:
linear inverse problem, continuous linear operator, integral operator, regularization, Banach space, locally convex space.
@article{MZM_2007_82_2_a8,
author = {L. D. Menikhes},
title = {On a {Sufficient} {Condition} for {Regularizability} of {Linear} {Inverse} {Problem}},
journal = {Matemati\v{c}eskie zametki},
pages = {242--246},
year = {2007},
volume = {82},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_2_a8/}
}
L. D. Menikhes. On a Sufficient Condition for Regularizability of Linear Inverse Problem. Matematičeskie zametki, Tome 82 (2007) no. 2, pp. 242-246. http://geodesic.mathdoc.fr/item/MZM_2007_82_2_a8/
[1] L. D. Menikhes, “O regulyarizuemosti nekotorykh klassov otobrazhenii, obratnykh k integralnym operatoram”, Matem. zametki, 65:2 (1999), 222–229 | MR | Zbl
[2] V. A. Vinokurov, “\begin{bad}O ponyatii regulyarizuemosti razryvnykh otobrazhenii\end{bad}”, ZhVMiMF, 11:5 (1971), 1097–1112 | MR | Zbl
[3] Kh. Shefer, Topologicheskie vektornye prostranstva, Mir, M., 1971 | MR | Zbl
[4] L. D. Menikhes, “O regulyarizuemosti otobrazhenii, obratnykh k integralnym operatoram”, Dokl. AN SSSR, 241:2 (1978), 282–285 | MR | Zbl