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.
Robert Grone, Peter D. Johnson, Jr. (1982)
Colloquium Mathematicae
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Peter D. Johnson, Jr. (1978)
Colloquium Mathematicae
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Tamminana Kurmayya, Koratti C. Sivakumar (2008)
Discussiones Mathematicae - General Algebra and Applications
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In this short note we study necessary and sufficient conditions for the nonnegativity of the Moore-Penrose inverse of a real matrix in terms of certain spectral property shared by all positive splittings of the given matrix.
Mostafa Mbekhta, Jaroslav Zemánek (2007)
Banach Center Publications
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Dragan S. Djordjević, Stanimirović, Predrag S. (2001)
Czechoslovak Mathematical Journal
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We investigate the generalized Drazin inverse and the generalized resolvent in Banach algebras. The Laurent expansion of the generalized resolvent in Banach algebras is introduced. The Drazin index of a Banach algebra element is characterized in terms of the existence of a particularly chosen limit process. As an application, the computing of the Moore-Penrose inverse in -algebras is considered. We investigate the generalized Drazin inverse as an outer inverse with prescribed range...
Irene Rousseau (2001)
Visual Mathematics
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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.
Ibrahim M. Nabiev (2014)
Colloquium Mathematicae
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The inverse problem of spectral analysis for the diffusion operator with quasiperiodic boundary conditions is considered. A uniqueness theorem is proved, a solution algorithm is presented, and sufficient conditions for the solvability of the inverse problem are obtained.
Benalili, Mohammed, Lansari, Azzedine (2005)
Lobachevskii Journal of Mathematics
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J. Koliha, V. Rakočević (1998)
Studia Mathematica
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We study the continuity of the generalized Drazin inverse for elements of Banach algebras and bounded linear operators on Banach spaces. This work extends the results obtained by the second author on the conventional Drazin inverse.