Spectral reduction of compact normal operators
The spectral theory and its applications. Generalities and compact operators

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Spectral reduction of compact normal operators
The spectral theory and its applications. Generalities and compact operators

Author : Marc LENOIR

Publication date: April 10, 2010 | Lire en français

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4. Spectral reduction of compact normal operators

A model for this is provided by Fourier series decomposition. If we denote S1 the unit circle, then for θ ∊ S1, the functions einθ, n∈ℤ form a self-adjoint subalgebra of C0 (S1) that separates the points, so it is dense in C0 (S1) by virtue of Stone-Weierstraβ's theorem. In other words, any continuous periodic function f is the sum of a uniformly convergent series of the form f(θ)=∑n∈ℤane

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