Robin Harte, Mostafa Mbekhta (1993)
Studia Mathematica
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Commutativity and continuity conditions for the Moore-Penrose inverse and the "conorm" are established in a C*-algebra; moreover, spectral permanence and B*-properties for the conorm are proved.
M. I. Belishev, V. Yu. Gotlib, S. A. Ivanov (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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This work is devoted to numerical experiments for multidimensional Spectral Inverse Problems. We check the efficiency of the algorithm based on the BC-method, which exploits relations between Boundary Control Theory and Inverse Problems. As a test, the problem for an ellipse is considered. This case is of interest due to the fact that a field of normal geodesics loses regularity on a nontrivial separation set. The main result is that the BC-algorithm works quite successfully...
Trung Dinh Tran (2002)
Applications of Mathematics
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The paper defines and studies the Drazin inverse for a closed linear operator in a Banach space in the case that belongs to a spectral set of the spectrum of . Results are applied to extend a result of Krein on a nonhomogeneous second order differential equation in a Banach space.
Zagorodnyuk, S. M. (2011)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 15A29. In this paper we introduced a notion of the generalized spectral function for a matrix J = (gk,l)k,l = 0 Ґ, gk,l О C, such that gk,l = 0, if |k-l | > N; gk,k+N = 1, and gk,k-N № 0. Here N is a fixed positive integer. The direct and inverse spectral problems for such matrices are stated and solved. An integral representation for the generalized spectral function is obtained.
Guillaume Bal (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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This paper deals with the homogenization of a spectral equation posed in a periodic domain in linear transport theory. The particle density at equilibrium is given by the unique normalized positive eigenvector of this spectral equation. The corresponding eigenvalue indicates the amount of particle creation necessary to reach this equilibrium. When the physical parameters satisfy some symmetry conditions, it is known that the eigenvectors of this equation can be approximated...
Amin Boumenir (2014)
ESAIM: Control, Optimisation and Calculus of Variations
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We show that we can reconstruct two coefficients of a wave equation by a single boundary measurement of the solution. The identification and reconstruction are based on Krein’s inverse spectral theory for the first coefficient and on the Gelfand−Levitan theory for the second. To do so we use spectral estimation to extract the first spectrum and then interpolation to map the second one. The control of the solution is also studied.
Mostafa Mbekhta, Jaroslav Zemánek (2007)
Banach Center Publications
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V. Dinakar, N. Barani Balan, K. Balachandran (2017)
Nonautonomous Dynamical Systems
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We consider the reaction-diffusion equation with discontinuities in the diffusion coefficient and the potential term. We start by deriving the Carleman estimate for the discontinuous reaction-diffusion operator which is deployed in the inverse problems of finding the stability result of the two discontinuous coefficients from the internal observations of the given parabolic equation.
Irene Rousseau (2001)
Visual Mathematics
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Benalili, Mohammed, Lansari, Azzedine (2005)
Lobachevskii Journal of Mathematics
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Y. Daikh, W. Chikouche (2016)
Commentationes Mathematicae Universitatis Carolinae
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We are interested in the discretization of the heat equation with a diffusion coefficient depending on the space and time variables. The discretization relies on a spectral element method with respect to the space variables and Euler's implicit scheme with respect to the time variable. A detailed numerical analysis leads to optimal a priori error estimates.