# Questions tagged [spectral-theory]

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

2,714 questions
Filter by
Sorted by
Tagged with
19 views

### 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 ...
27 views

### 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?
28 views

### 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 ...
52 views

1 vote
62 views

33 views

### 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 ...
1 vote
28 views

95 views

### 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 ...