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Title: Criteria of the Uniqueness of Solutions and Well-Posedness of Inverse Source Problems

Abstract

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.

Authors:
 [1]
  1. National Research Nuclear University MEPhI (Moscow Engineering Physics Institute) (Russian Federation)
Publication Date:
OSTI Identifier:
22771255
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Sciences
Additional Journal Information:
Journal Volume: 230; Journal Issue: 6; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; DIFFERENTIAL EQUATIONS; FUNCTIONS; HILBERT SPACE; MATHEMATICAL SOLUTIONS

Citation Formats

Kostin, A. B., E-mail: abkostin@yandex.ru. Criteria of the Uniqueness of Solutions and Well-Posedness of Inverse Source Problems. United States: N. p., 2018. Web. doi:10.1007/S10958-018-3799-8.
Kostin, A. B., E-mail: abkostin@yandex.ru. Criteria of the Uniqueness of Solutions and Well-Posedness of Inverse Source Problems. United States. doi:10.1007/S10958-018-3799-8.
Kostin, A. B., E-mail: abkostin@yandex.ru. Tue . "Criteria of the Uniqueness of Solutions and Well-Posedness of Inverse Source Problems". United States. doi:10.1007/S10958-018-3799-8.
@article{osti_22771255,
title = {Criteria of the Uniqueness of Solutions and Well-Posedness of Inverse Source Problems},
author = {Kostin, A. B., E-mail: abkostin@yandex.ru},
abstractNote = {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.},
doi = {10.1007/S10958-018-3799-8},
journal = {Journal of Mathematical Sciences},
issn = {1072-3374},
number = 6,
volume = 230,
place = {United States},
year = {2018},
month = {5}
}