Reconstruction of a convolution operator from the right-hand side on the semiaxis
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Anatoly F. Voronin
Abstract
In this paper, a Volterra integral equation of the first kind in convolutions on the semiaxis when the integral operator kernel and the right-hand side of the equation have a bounded support is considered. An inverse problem of reconstructing the solution to the equation and the integral operator kernel from values of the right-hand side is formulated. Necessary and sufficient conditions for the inverse problem solvability are obtained. A uniqueness and stability theorem is proved. Explicit formulas for reconstruction of the solution and kernel are obtained.
Funding source: RFBR
Award Identifier / Grant number: 13-01-00275
The author would like to thank Professor S. I. Kabanikhin and Professor Y. E. Anikonov for useful discussions of this paper. It should also be noted that both this paper and [J. Appl. Ind. Math. 8 (2014), no. 3, 428–435] were made after a discussion with S. I. Kabanikhin of the question of applying the Volterra equation of the first kind in convolutions and the Inverse Problem (A) in geophysics.
© 2015 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Identification of nonlinear heat conduction laws
- Numerical solution of the multidimensional Gelfand–Levitan equation
- On generalized cross validation for stable parameter selection in disease models
- An optimal regularization method for convolution equations on the sourcewise represented set
- Multilevel Jacobi and Gauss–Seidel type iteration methods for solving ill-posed integral equations
- Estimation of distributed parameters in permittivity models of composite dielectric materials using reflectance
- Asymptotic method for finding the coefficient of hydraulic resistance in lifting of fluid on tubing
- Identification of biological models described by systems of nonlinear differential equations
- Statistical inversion in electrical impedance tomography using mixed total variation and non-convex ℓp regularization prior
- Reconstruction of a convolution operator from the right-hand side on the semiaxis
- International workshop “Inverse Problems and Integral Geometry” Immanuel Kant Baltic Federal University, Kaliningrad, Russia October 13–16, 2014
Artikel in diesem Heft
- Frontmatter
- Identification of nonlinear heat conduction laws
- Numerical solution of the multidimensional Gelfand–Levitan equation
- On generalized cross validation for stable parameter selection in disease models
- An optimal regularization method for convolution equations on the sourcewise represented set
- Multilevel Jacobi and Gauss–Seidel type iteration methods for solving ill-posed integral equations
- Estimation of distributed parameters in permittivity models of composite dielectric materials using reflectance
- Asymptotic method for finding the coefficient of hydraulic resistance in lifting of fluid on tubing
- Identification of biological models described by systems of nonlinear differential equations
- Statistical inversion in electrical impedance tomography using mixed total variation and non-convex ℓp regularization prior
- Reconstruction of a convolution operator from the right-hand side on the semiaxis
- International workshop “Inverse Problems and Integral Geometry” Immanuel Kant Baltic Federal University, Kaliningrad, Russia October 13–16, 2014
