# 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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### Spectrum of 'separable' operator over measure spaces

Given $\sigma$-finite measure spaces $(X,\mu)$ and $(Y,\nu)$, can we say something about the spectra of operators on $A\in L^2(X\times Y; \mu\times \nu)$, if $A$ has a seprable sturcture? Something ...
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### Good source to study the Laplace transform.

I am studying the theory of semigroups and its links with the spectral theory and the Laplace transform turns out to be the intermediary between the two. Any suggestions for good sources?
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### maximal eigenvalue of self-adjoint operator is non-degenerate

I want some help in this one, if someone can prove or disprove it: "If $T$ is a compact, self-adjoint operator with positive spectral gap, then $||T||_2$ is always an eigenvalue and the ...
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### Size of essential spectrum if $T-\lambda$ is not injective for all $\lambda$ in the essential spectrum.

Let $B$ be some Banach space and let $T:B \to B$ be linear and bounded. I write $\sigma_e$ for the essential spectrum, i.e. the set of $\lambda \in \mathbb{C}$ s.t. $T-\lambda$ is not Fredholm. The ...
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### Good books and lecture notes to learn pseudo-differential operators and spectral theory

I am looking for a list of good books and lecture notes to learn pseudo-differential operators and spectral theory (for infinite dimensions.) I am familiar with introductory functional analysis, ...
I am trying to find an upper bound for the maximum distance between 2 vectors that satisfy $$x, y \in \{s|As \geq 0 \text{ and } \lvert \lvert s \rvert \rvert_2 \leq L\}$$. What is the maximum ...
I understand that the continuous spectrum of an operator are the $\lambda's$ such that $(\lambda-T)$ is injective but ran$(\lambda-T)$ isn't dense in the image. But i can't properly calculate it for a ...