Spectral attributes of self-adjoint fredholm operators in hilbert space: a rudimentary insight
In defining the finiteness or infiniteness conditions of discrete spectrum of the Schrodinger operators, a fundamental understanding on n(1 , F(·)) is crucial, where n(1, F) is the number of eigenvalues of the Fredholm operator F to the right of 1. Driven by this idea, this paper provided the invert...
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| Main Authors: | , |
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| Format: | Article |
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Birkhauser Verlag AG
2019
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| Online Access: | http://eprints.utm.my/id/eprint/88486/ http://www.dx.doi.org/10.1007/s11785-018-0865-7 |
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| Summary: | In defining the finiteness or infiniteness conditions of discrete spectrum of the Schrodinger operators, a fundamental understanding on n(1 , F(·)) is crucial, where n(1, F) is the number of eigenvalues of the Fredholm operator F to the right of 1. Driven by this idea, this paper provided the invertibility condition for some class of operators. A sufficient condition for finiteness of the discrete spectrum involving the self-adjoint operator acting on Hilbert space was achieved. A relation was established between the eigenvalue 1 of the self-adjoint Fredholm operator valued function F(·) defined in the interval of (a, b) and discontinuous points of the function n(1 , F(·)). Besides, the obtained relation allowed us to define the finiteness of the numbers z∈ (a, b) for which 1 is an eigenvalue of F(z) even if F(·) is not defined at a and b. Results were validated through some examples. |
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