Muminov, M. I. and Ghoshal, S. K.
(2019)
*Spectral attributes of self-adjoint fredholm operators in hilbert space: a rudimentary insight.*
Complex Analysis and Operator Theory, 13
(3).
pp. 1313-1323.
ISSN 1661-8254

Full text not available from this repository.

Official URL: http://www.dx.doi.org/10.1007/s11785-018-0865-7

## Abstract

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.

Item Type: | Article |
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Uncontrolled Keywords: | discrete spectrum, essential spectrum, fredholm analytic theorem |

Subjects: | Q Science > QA Mathematics > QA75 Electronic computers. Computer science |

Divisions: | Science |

ID Code: | 88486 |

Deposited By: | Narimah Nawil |

Deposited On: | 15 Dec 2020 08:06 |

Last Modified: | 15 Dec 2020 08:06 |

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