Titlebook: Basic Operator Theory; Israel Gohberg,Seymour Goldberg Textbook 2001 Birkh?user Boston 2001 Applications of Mathematics.Functional Analysi

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Hilbert Spaces,In this chapter we review the main properties of the complex n-dimensional space ?. and then we study the Hubert space which is its most natural infinite dimensional generalization. Many applications to classical problems are included (Least squares, Fourier series and others).

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Spectral Theory of Compact Self Adjoint Operators,One of the fundamental results in linear algebra is the spectral theorem which states that if . is a finite dimensional Hubert space and A ∈ .(.) is self adjoint, then there exists an orthonormal basis φ.,…, φ. for . and real numbers λ.,…, λ. such that ..

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