Geodesic
Criteria of the uniqueness of solutions and well-posedness of inverse source problems
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Functional analysis, Tome 133 (2017), pp. 81-119

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In this paper, we study the relation between the well-posedness of the inverse problem of the recovering the source in an abstract differential equation and the basis property of a certain class of function systems in a Hilbert space. As a consequence, based on the results concerning the well-posedness of inverse problems, we obtain the Riesz basis property and—under certain additional conditions—the Bari basis property of such systems.
Keywords: inverse problem, equation in Hilbert space, well-posedness, completeness, Riesz basis property.
Mots-clés : final observation 
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     author = {A. B. Kostin},
     title = {Criteria of the uniqueness of solutions and well-posedness of inverse source problems},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {81--119},
     publisher = {mathdoc},
     volume = {133},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_133_a1/}
}
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A. B. Kostin. Criteria of the uniqueness of solutions and well-posedness of inverse source problems. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Functional analysis, Tome 133 (2017), pp. 81-119. http://geodesic.mathdoc.fr/item/INTO_2017_133_a1/