# Tagged Questions

Spectral theory is the study of generalized notions of eigenvalues and eigenvectors for linear operators in Banach spaces.

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### Proving two stubborn inequalities for completely positive maps in C*-algebras

I recently came across this in my studies of functional analysis in C* algebras which got me stuck: For a completely positive map between C* algebras $\phi : A \to B$ we are to prove these two ...
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### Coefficients of the eigenfunction

Related to the question : Eigenvalues of the circle over the Laplacian operator, how is it possible to find $c_1$ and $c_2$ related the explicit function $g(x)=c_1 \cos (\mu x)+ c_2 \sin (\mu x)$? ...
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### Laplace-Beltrami operator on a circle - Explanation

I would like to find the spectrum of a circle. I know that the Laplace-Beltrami eigenvalue problem for unit circle is equivalent to the regular Laplacian eigenvalue problem for the interval of the ...
### The particularity of $k$ being an integer in the solution of a DE
Related to the Thomas's comment in the question : Eigenvalues of the circle over the Laplacian operator, is there anyone could tell me why the periodic function $g$ has a fundamental set of solutions ...
Consider the operator $L:L^1(S^1)\to L^1(S^1)$ given by $$(Tf)(x)=\dfrac{1}{2}\left( f\left( \dfrac{x}{2}\mod 1\right)+f\left( \dfrac{x+1}{2} \mod 1 \right) \right)$$ where we identified $S^1$ with ...