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Mathematics > Spectral Theory

arXiv:1504.06052 (math)
[Submitted on 23 Apr 2015]

Title:Solution of the inverse spectral problem for a convolution integro-differential operator with Robin boundary conditions

Authors:S.A. Buterin, A.E. Choque Rivero
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Abstract:The operator of double differentiation on a finite interval with Robin boundary conditions perturbed by the composition of a Volterra convolution operator and the differentiation one is considered. We study the inverse problem of recovering the convolution kernel along with a coefficient of the boundary conditions from the spectrum. We prove the uniqueness theorem and that the standard asymptotics is a necessary and sufficient condition for an arbitrary sequence of complex numbers to be the spectrum of such an operator. A constructive procedure for solving the inverse problem is given.
Comments: 10 pages
Subjects: Spectral Theory (math.SP)
MSC classes: 34A55, 45J05, 47G20
Cite as: arXiv:1504.06052 [math.SP]
  (or arXiv:1504.06052v1 [math.SP] for this version)
  https://doi.org/10.48550/arXiv.1504.06052
Journal reference: Applied Mathematics Letters 48 (2015) 150-155
Related DOI: https://doi.org/10.1016/j.aml.2015.04.003

Submission history

From: Sergey Buterin [view email]
[v1] Thu, 23 Apr 2015 06:24:12 UTC (9 KB)
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