S. A. Buterin, “Inverse spectral reconstruction problem for the convolution operator perturbed by a one-dimensional operator”, Mat. Zametki, 80:5 (2006), 668–682; Math. Notes, 80:5 (2006), 631

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Matematicheskie Zametki, 2006, Volume 80, Issue 5, Pages 668–682
DOI: https://doi.org/10.4213/mzm3076 (Mi mzm3076)

This article is cited in 15 scientific papers (total in 15 papers)

Inverse spectral reconstruction problem for the convolution operator perturbed by a one-dimensional operator

S. A. Buterin

Saratov State University named after N. G. Chernyshevsky

Full-text PDF (497 kB) Citations (15)

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DOI: https://doi.org/10.4213/mzm3076

Abstract: We consider a one-dimensional perturbation of the convolution operator. We study the inverse reconstruction problem for the convolution component using the characteristic numbers under the assumption that the perturbation summand is known a priori. The problem is reduced to the solution of the so-called basic nonlinear integral equation with singularity. We prove the global solvability of this nonlinear equation. On the basis of these results, we prove a uniqueness theorem and obtain necessary and sufficient conditions for the solvability of the inverse problem.

Received: 04.10.2004

English version:
Mathematical Notes, 2006, Volume 80, Issue 5, Pages 631–644
DOI: https://doi.org/10.1007/s11006-006-0184-6

Bibliographic databases:

UDC: 517.984

Language: Russian

Citation: S. A. Buterin, “Inverse spectral reconstruction problem for the convolution operator perturbed by a one-dimensional operator”, Mat. Zametki, 80:5 (2006), 668–682; Math. Notes, 80:5 (2006), 631–644

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Linking options:

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https://doi.org/10.4213/mzm3076

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This publication is cited in the following 15 articles:

S. A. Buterin, “On the Uniform Stability of Recovering Sine-Type Functions with Asymptotically Separated Zeros”, Math. Notes, 111:3 (2022), 343–355
S. A. Buterin, “Inverse Spectral Problem for Integro-Differential Sturm–Liouville Operators with Discontinuity Conditions”, J Math Sci, 263:6 (2022), 741
Buterin S., “Uniform Stability of the Inverse Spectral Problem For a Convolution Integro-Differential Operator”, Appl. Math. Comput., 390 (2021), 125592
Buterin S., “Uniform Full Stability of Recovering Convolutional Perturbation of the Sturm-Liouville Operator From Thespectrum”, J. Differ. Equ., 282 (2021), 67–103
Sergey Buterin, Trends in Mathematics, Transmutation Operators and Applications, 2020, 337
Buterin S., Yurko V., “Inverse Problems For Second Order Integral and Integro-Differential Operators”, Anal. Math. Phys., 9:1 (2019), 555–564
Buterin S., “An Inverse Spectral Problem For Sturm-Liouville-Type Integro-Differential Operators With Robin Boundary Conditions”, Tamkang J. Math., 50:3, SI (2019), 207–221
Buterin S.A., Vasiliev S.V., “On Uniqueness of Recovering the Convolution Integro-Differential Operator From the Spectrum of Its Non-Smooth One-Dimensional Perturbation”, Bound. Value Probl., 2018, 55
Yurko V., “Inverse Problems For Arbitrary Order Integral and Integro-Differential Operators”, Results Math., 73:2 (2018), UNSP 72
Buterin S., Malyugina M., “On Global Solvability and Uniform Stability of One Nonlinear Integral Equation”, Results Math., 73:3 (2018), UNSP 117
S. A. Buterin, “Obratnaya spektralnaya zadacha dlya integro-differentsialnykh operatorov Shturma–Liuvillya s usloviyami razryva”, Trudy Krymskoi osennei matematicheskoi shkoly-simpoziuma, SMFN, 64, no. 3, Rossiiskii universitet druzhby narodov, M., 2018, 427–458
Buterin S.A., Pikula M., Yurko V.A., “Sturm-Liouville Differential Operators With Deviating Argument”, Tamkang J. Math., 48:1 (2017), 61–71
V. A. Yurko, “Inverse Problems for First-Order Integro-Differential Operators”, Math. Notes, 100:6 (2016), 876–882
Buterin S.A., Choque Rivero A.E., “on Inverse Problem For a Convolution Integro-Differential Operator With Robin Boundary Conditions”, Appl. Math. Lett., 48 (2015), 150–155
Buterin S.A., “On the reconstruction of a convolution perturbation of the Sturm-Liouville operator from the spectrum”, Differ. Equ., 46:1 (2010), 150–154

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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