# Questions tagged [spectral-theory]

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

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### I need to find the spectrum of an operator.

I need to prove that the spectrum of operator A in $L_{2}[0,1]$ is [-1;1] where $Ax(t) = \sin(\frac{1}{t})x(t)$ if $t > 0$ and$Ax(0) = 0$ Elementary - norm of $A$ is less or equal to $1$. Hence, ...
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### Spectral properties of hypercyclic operators

I'm studying some topics related to the invariant subspace problem, and consequently I find myself dealing with hypercyclic operators. (An operator $T:X\rightarrow X$ is hypercyclic if there is some ...
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### Some questions about wave operator.

On sec. 3.4.1 in Schlag & Nakanish: invariant manifolds and dispersive Hamiltionian evolution equations, the authors talked something about wave operators. The wave operators are defined as the ...
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### Laplacian and eigenvectors relationship

I have a Laplacian matrix $L_G$ of a connected and undirected graph $G$. $L_G$ is symmetric, positive semi-definite. I have another laplacian $L_H$, that is also symmetric and positive semi-definite, ...
I am reading the paper "Specra and Eigenforms of the Laplacian on $\mathbb{S}^n$ by Ikeda-Taniguchi and $\mathbb{P}^n(\mathbb{C})$" and i want to know where do i can get a proof or some ideas to prove ...