Spectral Theory of Bounded Self-Adjoint Linear Operators
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Date
2013-02
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Addis Ababa University
Abstract
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Spectral theory is very broad but important aspect of applied functional analysis which extends to eigenvectors and eigenvalue theory of a square matrix. The name was introduced by David Hilbert in his original formulation of Hilbert space theory. It was later discovered that spectral theory could explain features of atomic spectral in quantum mechanics.
While solving the system of linear algebraic equations, differential equations or integral equations, we come across the problem related to inverse operation. Spectral theory is concerned with such inverse problems.
In this paper we consider the spectrum of a hermitian (or self-adjoint) operator. We also study the Hilbert-adjoint operator of the bounded linear operator and the Riesz representation of bounded linear functional by inner products
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Spectral Theory of Bounded